Yes you can play more than one at a time on a 15 amp circuit. You must be pretty skilled if you can play more than one
game at a time.

Depends what you have on the circuit already that you'll need to take into consideration. On average they pull about 2.5A. I'd use that to determine games per circuit. 15A breaker at 80% is 12A. So, you'd be safe with probably 4 or 5. On a 20A circuit at 80% is 16A. So, around 6 or 7 games per circuit.

I’ve got 6 lit up now all ready to play on a 15amp breaker. Never a problem.

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If you're planning to used a switched circuit or power strip to turn multiple games on at once beware that the initial or inrush current can be much higher than the nominal or steady state current (which is sometimes specified on the schematic). So the current required to turn on several games at the same time can be much higher than the current required turning on those same games one at a time.

More info at https://en.wikipedia.org/wiki/Inrush_current

/Mark

While two flipper coils are moving through their hot-winding-only part of the stroke, I have measured a draw of over 6 amps for the game as a whole, with incandescent bulbs.
.................David Marston