IIRC...
The A1 and A2 had identical beds, only differences were the addition of the surge brake system and change to 8x6.5 lugs to match the CUCV.
The A3 received the wider track to match the HMMWV, stronger axle, stronger springs, newly designed landing leg, and strengthened frame (3"-4"). These modifications bumped the trailer to 1t XC capacity. To accommodate the wider track, the wheels were pushed further out, subsequently pushing the fenders out as well giving ~48" between inside the bed.
Some A2s were retrofitted with the A3 running gear, but no modifications were made to the frame or bed to bring these to proper A3 spec. This was done as a band-aid, and these trailers do show up on GL every once in a while.
There were some A2s that had stronger frames and bigger leaf packs, and identified the a2e1. These enhanced trailers were typically gen-sets for the 5kw generators. While many remained as M116a2e1 chassis, there were a few built with full beds/tarps/bows designated M101a2 (though the correct nomenclature should have been M101a2e1).
External dimensions for the M101, a1, and a2 should be the same, along with mounting points. We used to hodgepodge trailers together from what we could find at DRMO and later the scrap yard at Udari before the push north. The A3 bed will fit, but the fenders will stick wide, and the inside of your tires will rub. The only real concern is if the bed is actually for the M105 series of trailers. The beds looks similar, but the frame rails are in different locations, and the box will hang just a bit further aft. The M105 box is also a tad heavier than the M101 as well.
on edit:
The M101 and M101a1 beds were phased out in recent years and replaced with the a2 or a3 boxes. These new boxes were fitted with lifting loops at all four corners, looks like a u-bolt facing up) so they could be hoisted without spreader bars (per TM).
Here is an M101a1 with the a2 bed mounted...
You can see these lifting rings. Ironically enough, the 8-lug on the trailer behind denotes an a2 configuration, yet it has an a1 bed!
If you want, shoot me a link to the beds you are looking at, and I can help ya ID if they are exactly what you are looking for.