Crossover:
No.

Timeline:
Begins during Fourth Year.

Alterations to Canon:
Yes.

Given the emphasis and importance of fertility rites in religions and pagan rituals from ancient times it would be reasonable to infer that sex and magic are intertwined. This, of course, isn't something built into the world of a series of childrens' books.

Pairings:
Harry/Hermione
Harry/Multi
Harry/Harem

Possible extensive femslash.

Background:

In this world certain specific talents and abilities run in particular bloodlines. Over the many generations certain families have acquired skills and become able to do certain magic that non-family members cannot do or can do some magic far more easily and skillfully for far less effort than a non-family member could hope to do.

For a comparison think of it as a much lesser version of the 'blood limits' of Naruto.

In some families the gifts might be minor but appear in every member of the family line (except squibs) while in another family the gift might only appear in one or two members of each generation, if that. Some families do not have consistent gifts, with several different ones known to appear seemingly at random in their members and some even have secondary blood gifts, a further mutation that can emerge which for some means an even greater talent or a curse where the gift turns against them with sickness or madness.

The effect of these blood gifts are the influence they have on the political, social and economic aspects of the wizarding world. Each gift may lend to that family an advantage in business, battle, politics, fame and so on. Pureblood supremacists believe (wrongly) that muggles and muggleborns marrying into these bloodlines destroys or weakens them and have been known to resort to incest to literally keep it in the family. There are rituals, spells and potions to ensure that blood gifts can be suppressed in members of one family marrying into another, so that blood gifts are kept mostly separate, though there are always effects of blood from one line being blended into another.

Muggleborns are far less likely to develop their own blood gifts but it has been known to happen, though often not until later in life, past child-bearing age for witches. On the other hand the same rituals and spells which can keep blood gifts separate can also be used the opposite way, ensuring a witch who marries into a family absorbs some of their gifts. Most of these spells, potions and rituals involve or take place during sex and the exchange of fertility magic that is involved.

Fertility magic obeys certain rules. Wizards are 'expressive' and 'deconstructive', they expel (but don't typically absorb) fertility magic during sex and while their fertility magic can be combined with the fertility magic of witches, it tends to cancel out the fertility magic of other wizards. Witches on the other hand are 'receptive' and 'constructive', they mostly absorb (but also do expel some) fertility magic during sex and they can combine their fertility magic both with wizards and with other witches.

There are many consequences of these facts. The combined fertility magic of a single witch and wizard almost always is greater than the combined fertility magic of any three or four witches but there's only a 'logistics cap' on how many witches can combine their fertility magic, physical limitations and the preparation of rituals, so witches can collectively work great magic through witch-only covens. The ultimate combination is witches gathering magic from wizards and combining it between themselves and several aligned or allied political blocs of magical families do have their witches form covens to work spells together for the benefit of all the family members.

For individual witches there is another important reality of the overlap between fertility magic and blood gifts. A witch can perform a sex ritual to absorb fertility magic from a strong wizard (who hasn't come into his own blood gift yet) and jump start the emergence of her blood gift rather than waiting for it to emerge naturally. When this coincides with her deflowering it also often comes with a (typically) small but measurable increase in her total magical capacity, a permanent boost to her strength.

While there's no fixed timetable for when a witch must make the choice and perform the rite the accepted wisdom, part data and part anecdote, is that on or just after her birthday either when she is 15 or 16 years of age - meaning usually while she's at Hogwarts. Likewise the wizard she chooses must not have developed his own blood gift yet (most wizards of families with established gifts develop theirs before or shortly after they graduate) so is usually chosen from among her fellow students.

Consequently there's a great deal of concern and information gathering and trading among witches to identify the wizards with the greatest magical strength who haven't yet expressed their family gift. It's not uncommon for each year to see a small number of rather lucky wizards in fifth, sixth or seventh year being contracted to deflower many of the witches in their fourth, and yes 'contracted' because the witches typically wish confidentiality.

Story:

Hermione and her fellow witches are gathered the morning after the Welcoming Feast in 3rd year to inform them of the relevant facts. Most of the witches from pureblood and half-blood backgrounds have already been filled in by their families over the previous summer or even earlier, so it is mostly the muggleborns who are in for a surprise of what kinds of things go on concerning blood gifts and sex magic - something not covered in any real detail until 6th year.

They are informed that if they chose to undergo the ritual they must create a short list of wizards that they find acceptable choices and submit it at least two weeks before their 15th birthday as well as what kind of confidentiality they want. Madam Pomfrey will contact each wizard, have them sign a contract which binds him to keep her name confidential before he is informed of who requested him, even if he refuses. Hermione puts the actual choosing largely out of her mind other than discussing it with Parvati and Lavender and doing her own research through out the year.

There's a black market of information traded among witches, information gathered from Madam Pomfrey's own files and spells cast on wizards while they aren't paying attention that are supposed to give some indication of their strength - though no one really gives any consideration to the students in the lower years, being so young and underdeveloped physically and with no realistic chance that they'd be magically powerful as an upperclassman. Hermione decides she doesn't care about that so much, only that if she is going to have sex with a wizard it has to be someone she trusts and cares about... which pretty much narrows it down to Harry. Accordingly on the last day of term she passes her one-name list to Madam Pomfrey.

The wizards got a similar lecture from Madam Pomfrey the day after the witches received theirs. The responsibilities and traditions involved, the expectations that they respect and not mistreat witches concerning their upcoming 15th birthdays or afterwards, nor make any assumptions concerning any witches that because they were selected for her ritual that she would welcome anything more than that after the fact. Most of the pureblood wizards there know it probably won't matter for them for years, since witches usually chose more powerful upperclassmen not fellow year mates, simultaneously reassuring some and disappointing others.

Harry gives it no further thought except when the guys in their dorm room speculate about the witches in the year above them and which wizard got lucky with who.

Consequently Harry is in for a surprise when Arthur is the one to take Harry aside on the first night after his arrival at the Burrow that summer, providing him with a contract telling him that a witch has chosen him. After discussing it with Arthur for a while, who really does a fair bit of filling in the gaps in Harry's knowledge of the birds and the bees, Harry agrees and signs and is told Hermione is the witch who has chosen him. Harry finds Hermione (who is already at the Burrow) and they talk, Hermione explains she chose him because she trusts him.

They both think they have until September 19th to get used to the idea when Hermione is reminded that she used a time-turner to go back in time 6 hours a week for about 40 weeks the previous year, meaning she's about 10 days older than the calendar says she is. They perform the ritual and manage to keep their promise not to be awkward or stop being friends because of it, instead becoming much closer and both are dancing around the possibility of starting an actual relationship.

Ron cottons on eventually and is a confused mess of upset and embarrassed.

What no one realised is that Harry is magically the strongest student at Hogwarts and has been since the Chamber of Secrets/Dementor on the Express when Voldemort's horcrux was removed from him by the Basilisk Venom/Dementor. Hermione's magic is MUCH stronger over the following few days and ends up frustrated fending off many witches who want to know who she picked, considering the results of her ritual. People have their suspicions but don't press... until Hermione demonstrates a powerful blood gift almost immediately.

Lavender has her birthday coming up and asks Hermione's permission before requesting Harry (because of course you picked Harry!), surprising Hermione a great deal at Lavender's consideration and making her feel quite guilty about wanting to say no to Lavender. Lavender assures she won't try to take Harry away from Hermione if she's worried about that and Hermione gives her permission. Lavender subsequently demonstrates the same huge magical boost and awakens the Brown family's blood gift immediately, leading to a deluge of witches from 4th year requesting Harry suspecting, correctly, he is the wizard responsible.

Further:

Many witches having their turn with Harry, some standoffish and clinical/formal, others wanting an intimate and comfortable first time, some girls sharing the same birthday like Padma and Parvati, some nervous because they prefer girls, some of the fifth year girls who waited for their 16th birthday. Jealousy from other blokes in his year and above who realise they are not going to be picked.

The events of the Triwizard Tournament coming into play.
Hermione and Harry's relationship developing despite the complications.
Hermione becoming involved in coven magic with other witches deflowered by Harry.
There are, lesser, but not insignificant advantages to wizards who perform the ritual with witches and Harry being chosen so frequently sees him accumulate those magical benefits.
Late sixth or seventh year Harry receives the Potter family blood gift (nothing particular in mind) but it is a great deal more powerful than should be expected, both from his own power and all the rituals he participated in.
How many witches remain a permanent fixture in his love life and how many just friendly acquaintances or go back to being total strangers?