Hi, there! I'm a newcomer to ArM and was curious if there were any precedents for magi belonging to more than one House, or at least having access to more than one House's advantages by having a good enough reputation with them, or just under which context would this be possible if ever.
Thank you!
The only House that accepts dual membership is House Tytalus, and this usually causes problems among those that become involuntary members of the House. (No, they don't ask before admitting a member of some other House into House Tytalus. Where would the fun be in that?)
It is possible to change House, but that is mainly a matter of political/social choice.
The bonus virtue each House gives is due to the training during apprenticeship, so that won't change even if you change House.
There is actually a Virtue representing just this: Guest of the House. It's written for coming into House Criamon from another House. You build with a different House's Virtue(s) but are a member of House Criamon, without Enigmatic Wisdom. Theoretically you could use this in several other cases, even though it's just written for Criamon. Additionally there are canonical cases of apprentices being claimed by Bonisagus magi, so you might have a case where a Bonisagus magus has Faerie Magic, for instance. Finally, the vast majority of House Virtues are simply generally available anyway and so you can just take them.
Well, that is compromising, just taking someone in without bothering to explain the issue hahaha thank you!
ooooh that will be plenty useful, thank you!
Usually it is expected for a Magus to only be a member of one House at a time. Gaining membership in one means losing membership in the previous one. This is a rare but not unheard of occurrence. You could easily expect to find distinct lineages inside of any given House based on members that have beliefs/magic/traditions that come from different sources. The rules don't generally accommodate these sorts of ideas however.
They are just Virtues, you can buy those during character creation - or achieve them via Initiations, if you have access to TMRE.
Except for the Mystery virtues from the Mystery houses. While it is technically possible to learn those without being a member of the corresponding House, it is far from trivial.
Mea Culpa. You are of course correct.
Clearly I need to sleep more.
I concur. Merinita will gladly teach you Faerie Magic and Merinita Lore, if you go through the effort to find a suitable patron/teacher. As part of joining House Merinita... (usually).
And of course for at least two of those cases (Verditius and Bjornaer) there are real costs to the initiation, discouraging casual interest.
... and those two houses can be somewhat secretive as well ...
Unlike the Criamon, who'd probably be happy to initiate anyone willing to listen to their drivel for more than 20 minutes or so 
First, it is important to differentiate membership into two Houses and having House virtue from two different Houses. Dual membership has political meaning - who is a mage reporting to (you cannot serve two masters...) and depending on the house, they can have a strong view on that point, and some could not care less (House Ex Miscellanea for example).
A good background, discussion with the SG and the flaw Dark Secret and/or Tormenting Master, I am sure many combination of house virtue are possible at character creation. Many other virtues can be gained through initiations, and gaining some unique house virtues (Bjornaer and Verditius) without House initiation can be excellent story materials.
What if an Ancestral Beast initiated a mage or an apprentice outside of House Bjornaer in the Heartbeast Outer Mystery for its own purpose? (I personally would recommend to keep the restriction regarding familiar, at it makes sense in the meaning of having a Heartbeast).
Since the Automata mystery has been leaked out of the House Verditius, it is the proof that for at least some Inner Mysteries, it is not needed to have undergone the Outer Mystery initiation (Embrace of Boetius), and technically speaking, the one being initiated does not need to have a high score in Cult Lore (in fact, it can be debated if even a minimum score of one is needed), only the Mystagogue needs to be knowledgeable. Considering how upset was House Verditius when the Automata mystery was leaked, the mage having Inner House mystery knowledge would need to be very careful not to be harassed by endless wizard's wars, certamen and very likely the full political power of House Verditius.
Enigmatic Wisdom can be gained through Twilight experience, and I am sure Criamon mage will gladly share their knowledge to who is willing to listen to their philosophy.
Mutantum magic is usually in Mercere House mage only, but despite their best effort, some genealogy tree might have been forgotten, and a few generations later a apprentice, taken by another House mage, might start to show Mutantum abilities. If those abilities are confirmed a few year prior Gauntlet, when the apprentice is the most useful for his master, said master won't let him go, so he will be Gauntleted in another House. It is possible that later, House Mercere is going to approach him to join the Cult of Heroes, or even switch house. All that is good story seed material.
Unfair! It is quite explicit that you can join Criamon without even being willing to listen to their drivel.
I assume they have some kind of sign-up sheet, with a box you can tick for "No drivel". But anyone with the Quaesitors breathing down their neck is likely to sign without reading that far.
First of all, as a newcomer, you don't want to go there. It is either abusive power-gaming, or a very complex narrative which is best explored when you are familiar with typical situations.
... but we can try to satisfy your curiosity even so ...
As @Ezechiel3571 says, we must distinguish between house membership and house virtues. One step further, I would distinguish between mechanical advantages (virtues), social advantages (access to resources and political clout), and formal membership (with little real impact). Not all houses have social advantages, and not all have mechanical advantages, i.e. the house virtues are often neither universal nor exclusive to the house.
Asking for demonstrated precedence, I know of only two cases. Tytalus has already been mentioned. They adopt members who subscribe to their ethos, regardless of there house and regardless of whether they want to. This does not mean that they get the self-confident virtue, although that might a prerequisite, and there are other ways to gain it.
The other case is Guernicus who appoint quaesitores in all houses, thus granting almost all their social advantages. They also do not have any mechanical advantages.
Except for the fact that mechanical advantages are retained when one changes house, which is possible¹, I do not think that there are more precedence, even if many special cases can be imagined.
¹ except for entering True Lineages, and the fact that Bjornaer may hunt down those members joining another house
Each of the Houses is a family. The OoH looks at apprenticeship as parent and child, even going so far as to use basically those words. Add in the very long lifespans and it is possible to have grand parent, great grand parent, and great great grand parent all still alive. Then of course you have the equivalent of aunts/uncles (other Magi trained by the great parent) and their children. For some Houses which do fostering, things get even more complex.
To go along with that, you get some rather complex internal family politics which most outsiders nether know or understand. While some players might know how they function if they read all the books, your average Magus who is not a member of a House will have no idea how they function internally.
Then of course you have family secrets, with the Houses covering the full spectrum of how protective and secretive they are about them. The Mystery Houses tend to be the most secretive, some rather violently so. The Bjornaer are rather a "kill em" House, while the Criamon seem to give theirs away freely (but who really understands it?).
Precedents:
Obviously those are limited both in scope and legality, but it's all I can think of at the moment.
House Ex Miscellanea have also historically taken in magi orbi ("orphans" who started off in another house).
Basically the True Lineages (Bonisagus, Guernicus, Mercere and Tremere) won't take in anyone they haven't trained (though there's an argument that an apprentice snatched late in his training by a Bonisagus might have his original house's virtues and flaws), the Mystery Cults (Bjornaer, Criamon, Merinita and Verditius) might take anyone showing an appropriate interest and aptitude (though the process of initiation into the Outer Mystery will be... interesting), and the Societates might do anything (a particularly artistic mage might weasel his way into Jerbiton, for example). Emphasis on the "might" above; this is one of those things I would expect to vary from saga to saga. It's all about the internal and external politics of the Houses, and what works for one mage may well be a complete failure for another.
Interestingly enough about True Lineages, the main requisite to join them is to be hermetically descended from the Founder himself.
So you can have a Bonisagus who was banished or chose to leave his House (like the lineage of Hercynius; see Dankmar), go on to train his own apprentices, and generations later those apprentices could join House Bonisagus again, their lineage traces back to Bonisagus himself after all!
Of course, politics can easily happen to make this...difficult.