One eighth of an acre with neighbours on both sides, how many hives is too many?

Forage is almost never the limit in a suburb, because your bees are flying over a couple of miles of gardens and nobody's hives are alone out there anyway. The real limits are your neighbours' tolerance and your own inspection time. Three hives on an eighth of an acre is physically fine. Three hives inspected properly during swarm season is most of a Saturday, every Saturday, and that is what people actually run out of.

I run four on a slightly smaller plot than yours and it works, with caveats I would want you to know. Robbing is the thing that changes when you go past two. With one hive, a careless moment costs you nothing. With four sitting close together, a dropped frame or an open feeder in a dearth can set off a robbing frenzy that involves every colony you own and puts a cloud of agitated bees over your garden for an afternoon. That is the scenario that generates a neighbour complaint, not the day to day flying. Entrance reducers in autumn and never feeding in the open have kept mine calm.

Before the count, sort the flight path and the water, because those are what turn a hive into a neighbour problem. Put a hedge, a fence panel or even a tall trellis a couple of metres in front of the entrances so the bees have to climb immediately, and they will be well above head height by the time they cross your boundary. Then give them water on your side, closer than the pool, and keep it topped up from early spring before they establish the habit of going elsewhere. Bees fix on a water source and are hard to move off it once they have chosen, so being first matters more than being closer.

The part that is not optional and that nobody on the internet can answer for you: check what your municipality actually says, and whether your area requires registration of colonies. In some places there is a hive count limit tied to lot size, in others there are setback rules from boundaries, and in a fair few there is a registration requirement with the agricultural authority that people simply do not know about until there is a disease inspection. Your local association will know the rules for your area cold and will usually tell you in one phone call. That call is worth more than this entire thread.

Two on that lot, three if you have a real reason and a screened flight path. The constraint is your Saturdays and the pool, not the acreage.

I put four on a small lot in my second year and had a defensive colony among them by August. One hive being difficult is manageable. One difficult hive next to three others, all of which get agitated when you open the difficult one, meant I could not work them at all on a weekday evening. Requeening solved it, but I spent six weeks apologising to the people next door and I have kept the number down since.

I will disagree with three as a target. For a hobbyist on a small lot, two is the number that gives you almost all of the benefit: you get a comparison colony so you can tell whether a problem is the hive or the season, and you have somewhere to pull a frame of brood from when one goes queenless. Going from two to three adds work and risk without adding much you did not already have. I went to four one year because splits are exciting and spent the whole summer resenting it.