Currently, it is possible to spam the /tpa command to the same recipient multiple times (they receive a new request regardless if they have already been requested.) Instead, it should work like this:

1. Steve sends /tpa alex
2. Alex receives request for /tpaccept or /tpdeny
3. Steve sends /tpa alex again before Alex has responded to the request (and within the request timeout)
4. Alex should not receive another request

Optionally, /tpdeny could halt repeated /tpa requests (either use the request timeout or a new config option)

It does ignore chat, there should be a cool down because it is very annoying to get a million requests from players it completely fills the chat can nothing else can be seen. Yes tptoggle would work but what if you still want to get requests?

Can you not also /ignore or /tptoggle? Though I do like the idea you outlined with not getting an additional request when another is pending.

Yes this is annoying, no doubt.
I handled this on my server by adding command cost to tpa (Essentials supports this), and staff used toggled it off, however there really is no reason to again show that a request have been made, when it didn't time out yet or when it has been denied.

Well, it'd be nice to not have to /tptoggle for all players when it's just one player.

Or you could add /tptoggle (player name)

@RoboMWM you can just /ignore

I'm assuming that also ignores chat messages as well?

This has been fixed in 3245ce1. You can grab the fix from build 407 on the CI server.