The North Brunswick district still has one spot left, but it's week six and right before Easter so I can see why some teams wouldn't want to go there (only one of the regionals that MAR teams are attending is week 6). Twelve teams are currently signed up for a third district event in MAR.
I have data for what events each MAR team has gone to over the past three years.
2015
2014
2013
Here's the number of teams attending a regional/outside district for the past three years:
2015: 13 teams (two teams doing two outside events)
2014: 12 teams
2013: 12 teams (one team also did an extra district)
And the number of teams doing three districts:
2015: 12 teams
2014: 10 teams
2013: 3 teams (one team also did a regional)
Unfortunately I don't have similar data for the 2012 season (it's quite a pain to collect this info manually, so usually I'll just put a thread up and have other people post when somebody is going to a regional).
Anyway, it seems like the number of teams doing three districts has gone up while the number of teams going to a regional is pretty constant. (Overall MAR growth is pretty flat too. It went from 110 in 2013 to 121 in 2015).
I'm pretty sure that there were still open spots for third district events in 2013, as the Lenape district only held 32 teams that year but had 39 the next.
Also, here's the number of teams who declined their MAR champ bids:
2014: 5 teams (3 had already qualified for St. Louis, the highest rank decline was 2607 in 17th).
2013: 16 teams (4 had already qualified for St. Louis, the highest rank decline was 341 in 1st).
2012: 11 teams (3 had already qualified for St. Louis, the highest rank decline was 103 in 11th).
Looking at it now, it seems like a lot of those declines weren't from already being qualified. Rather they were probably from money issues. MAR had ~100k in grants they gave out last year for teams to go to MAR champs, but last I've heard that budget is getting reduced this year so we may see more declines again.