In America, many groups have loads of meetings. If you want to go to lots of meetings, you can do that within one group. If you want to do lots of service, you can do that within one group. The notion of having one home group works very well.
In the UK, in Australia, in many other places, most groups hold just one meeting. In London, there have been multi-meeting groups over the years, either slightly cult-y groups that set themselves apart from the rest of AA or groups at a particular time and place each weekday (the latter not being cult-y at all, I hasten to add). I've seen these multi-meeting groups first hand, and they're usually problematic. There can be a lack of responsibility for particular meetings, which become weak and badly run, and there is cross-subsidisation financially. They rarely stay such and usually eventually break apart into different groups.
In London, if we tried to apply the one-home-group principle and barred service at more than one group, two things would happen. Firstly, newcomers would be barred from doing service more than once a week, and secondly groups would struggle to find enough people to do service. Neither helps anyone.
So, in London, the culture is that you can do service at as many groups as you want. Knock yerself out, mate. Best to avoid being secretary/chair or treasurer at more than one group: too much power and responsibility, and a risk of becoming a little bit superior, mother hen, chief pot- and bottle-washer, and that does the groups and the individual no good at all. Under no circumstances become a GSR of more than one group, for similar reasons, but also because you cannot have one consciousness representing two groups: this deprives one of the groups a voice in AA (or, rather, they each have only half a voice), and, where the groups are divided on a matter, the GSR is in a difficult position. These questions are largely theoretical, however, and I've never seen actual trouble arise from a GSR representing two groups, but it is definitely bad form, so don't do it.
There are two caveats, however.
Firstly: do not vote in group conscience meetings affecting the fellowship beyond the group. This upholds the one-member−one-vote principle.
Secondly: maybe attend the business meetings of all of the groups that one attends and does service at, because that's the forum for discussion of service, but attend the group consciences, to discuss larger matters of general policy and finance, at only one of the groups. That might be good etiquette, to avoid any individual having too much say in the overall form and content of meetings in a particular town.
The first of these two caveats is hard and fast. No exceptions.
The second of these is malleable. In London, the suggested remedy works. In small places with just a few groups, that, too would be impracticable because there simply aren't enough people to do all of the work and all of the thinking, or the people who are there are young in recovery and do not have enough experience to run groups themselves, so everyone's experience needs to be pooled everywhere.
Which one is the home group? In one sense, all are. In another, only the one where one has decided to vote in group conscience questions on matters affecting the fellowship beyond the group is the home group. In London, the question of home group is a bit academic. One feels at home at all the meetings one is committed to attending each week and certainly at all the meetings one does service at. There are indeed people who very staunchly say their home group is X but attend only every other week, because they find better things to do. It's more important to treat a group as a home group and attend and take part properly than to have a brass plate announcing that somewhere is one's home group then treat it casually. Substance is more important than form.
The last point: if a town has five groups and five meetings, the above questions would be swept aside if they all became one group. However, one would simply generate a new set of problems. For many, obvious reasons, each meeting develops its own character and culture, and this will be at odds with the collective character culture across all the meetings and with the character and culture of the other meetings. The differences may be small or large but will be there. This will inevitably lead to conflict. One can have a two-tier system, where each meeting has its own business meeting to discuss matters affecting that meeting alone and the meetings club together for group conscience meetings to discuss matters affecting the group as a whole, e.g. treasury, GSR representation, public information, in rather the same way that business is divided between groups and intergroups, but this is complicated, particularly with treasury (some meetings not pulling their weight), and questions of what gets to be discussed at what level arise, which are hard to resolve. In other words, this solution merely changes the type of problem one is facing. It also gives rise to a very particular problem: the failing meeting. If each meeting is its own group, that question is resolved simply: either it can pay its rent or it can't. If it can't, that's the end of it; if it can, then obviously it's doing well enough to encourage people to put their hands in their pockets, so let it live and sort out its problems.
In short, the culture of multiple group membership is absolutely fine, as long as certain guardrails are in place to avoid any particular voice becoming too loud or important. It is really up to the individual to hold themselves back when there is such a risk, and trusting God and a good sponsor will achieve this.