I think that this map is congested enough for 2vs2's; let alone 3vs3's. The FRPs only add to the problem (by clogging up paths and reducing flanking opportunities).
Watching the 2x OKW and 2x USF battle it out in the south for the first 10 mins was like watching excerpts from The Great Battle of the Blobs. (a bit boring

)
Since I presume you were playing the Allies (not sure which guy, though), I would adapt my strategy as follows:
- Try to mix a Brit with the USF player, so that you have a suppression platform on each "lane"
- Otherwise, one of the USF players should tech to lieutenant (the 50cal is really really good nowadays; if you can live with Vickers, the 50cal is a breeze)
- Giving PIATs would have helped take take out that Schwerer truck faster
- Giving PIATs to ONE commando squad and sneaking it up would have helped take out that annoying Panzerwerfer
- No matter how much you would adapt though, nothing would help you vs CP + CT aura stacking + elephant/JT. Your CalliOP is the only ticket to dealing with that.
Also, I don't understand why people insist on building (and upgrading!!) Tommies on such congested maps. Tommies are nothing more than overpriced artillery fodder for attrition matches.
Giving those double Brens to the Airlanding officer would have gone a loooong way better. The airlanding officer gets the commando version of the Bren, and now becomes a very combat-capable unit (try it once and activate the charge bonus; you will see).