the high dB signal is where the FCC Will care.
You can of course saturate the entire spectrum, but that breaks every network, not just the SSIDs you’re "waging war" against, and will probably get you a visit by the FCC sooner or later.
Maybe you could broadcast thousands of spoofed BSSIDs; I have no idea about the legality of that, and the legitimate operator of the SSID might not find that too funny and take legal action against you as well, as that would be pretty transparent denial of service on a public band.
It’s not like anybody can "own" an SSID name, and if you’re using WPA, the only effect would be a few milliseconds longer of initial connection time per device.
Actively running a DoS against your neighbor might or might not be legal, but it sure is petty (and given the above, unnecessary).
But it will not work.