I'd be surprised if the A-10 got more than 3 teams in, but it's possible to get 3 at-large bids if a 4th team sneaks in and takes the auto-bid (Duquesne and Mason, for instance, have zero at-large chances unless they finish 1st or 2nd, but maybe one of them takes the auto-bid).
The automatic qualifiers make the NIT a crapshoot every year.
A-10 NIT bids by year:
2019: 1 (Davidson)
2018: 0
2017: 1 (Richmond)
2016: 3 (Bona, GW, Davidson)
2015: 2 (GW, Richmond)
2014: 0 (This is the year the A-10 had 6 NCAA tournament teams)