I heard that Powerline networking only works within the same "circuit".
What exactly determines what a "circuit" is?
Would this work across floors of a multifamily house where the electric metering is different across them?
Multi-floored with separate breaker boxes on each floor.
There are separate meters outside for each floor where each looks like some type of mechanism in a glass bulb.
What would be neat is high speed internet that comes through the power line.
it would take care of the rural areas that don't have access to decent high speed internet.
I have no answer for your question other than try it, but make sure you can return the item if it doesn't work in your situation.
If you open-up your main breaker panel (and I'm not suggesting you do this!) you will see there is one main conductor feeding the left side of your panel, and another feeding the right side. Each of these is 120volts AC, though they are out of phase i.e. when one's 60Hz cycle is Up, the other's is Down. The "bus" behind the circuit breakers alternates contacts left & right such that if you have e.g. an electric oven needing 240VAC it gets both 120vac feeds and distributes them to the oven.
Now, if you inject a powerline signal onto a circuit that is on one phase, and intend to receive it on a circuit that is on another phase, how does the signal make it across phases? If the oven's Off, that's no help. But if you have an electric water heater that's On, then the signal can find its way across the bus and to the other circuit.
To avoid this problem, of needing to have an appliance that bridges the 120vac circuits, you can buy a bridging capacitor and install it in your breaker panel and it will allow your signal to pass across these lines. In the absence of same, it has to go-out back up thru the meter to your transformer (wherever that is, though maybe you're lucky and it's close-by your house) and back again, and it's unlikely to have the strength left to work at the receiver.
Now, if you have two meters, but you're fed by the same transformer, the signals ought to cross-over the the 2nd metered household barring other interference. But you will almost certainly need a bridging capacitor in one of the two panels to help it along.
Here's another discussion about this, I'm not sure where to buy a bridging cap these days (I got one from Leviton years ago) and I don't recommend you install it yourself but rather have an electrician do it. Your other option is simply to make certain your Transmitter is on the same 120VAC phase as your Receiver and e.g. you could move wires in one of the two main panels to assure this:
Powerline, ethernet over powerlines question
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