With the stbd engine running, When I try to crank the port engine the stb engine will die . 31 Formula twin 540.s . Is it the battery switch ?

Efi?

1050 dominators ,thunderbolt ignition

Does it do the same doing the opposite (other engine first).

Clould be the battery switch/one dead battery. easy to check out

Sounds like your robbing electrical juice from the igintion system when trying to start the other motor....i would look at voltage output....maybe the alt is not charging????

yes sir the same

This is the reason that each engine should have it's own battery with it's own switch and some kind of cross over for emergencies. Sounds like your batterys are weak and when you crank the second engine the battery voltage falls to far and shuts down the ignition. It is more of a problem on EFI engines since the ECM's will shut down with too low of voltage but it can affect coils or ignition modules too.

Still happens when switch is on both batteries

Yeah it will, you need to segregate the engines from each other using 2 or 4 batterys and 2 switches, they have to be seperated from each other(atleast they should be) a battery, or two baterys can be strong enough to start and run an engine but not start a second with the first running already.