My experience with three-way fights in general is that typically one side gets caught in the middle and gets reamed, and then whoever took the most damage doing the reaming gets mopped up by the ultimate victor.

The last three-way I was involved in, the only damage my mechs took was five points to my C3 Master unit because it tripped crossing a river. I started out randomly behind a hill, and, though I was doing my best to get into the fight as quickly as I could (standing around watching the others beat on each other is the smart strategy, but it's not the fun strategy, and it was a one-off with no real consequences), it took me long enough to get the slow-ass 100-ton master unit up to the top of the hill that the other two players were well stuck in by the time it got a clear firing lane. And then I found a nice spot there on the ridgeline and just parked it. Meanwhile, my other mech, a 6/9 (with the TSM hot) 60-ton energy boat with the C3 slave charged in to close range and skirted around the outside of the fight at high speed, shooting (and mostly missing) with its MLs, and, more effectively, spotting for the Master, up on the ridgeline at long PPC range, and giving it 4s and 5s to hit with its PPCs and Gauss rifles.

My slave unit got shot at, but not much, because the other players generally had better targets (each other), and never actually got hit, because it was most of the time moving like a light mech. The master unit never even so much as got shot at. Ended up just gunning down the one shambling wreck - a TSM Atlas variant - that made it out of the brawl in the middle as it tried to close through the master's vastly superior weapons range.