There likely aren't any. Over a year ago, I did a long search, through all the major brands - and virtually without exception, either their warranty was void or they explicitly stated "not for use on a trailer", for any kind of rack, 1,2 or more bikes. Unfortunately, you usually have to download the manual for the specific model, and read the disclaimers in the beginning pages to find that out.
Swagman makes two rated for trailer use - both 2 bike only models. Most of their models are not so rated.
1UpUSA makes a 2 bike model that at the time they said was usable on a trailer. Don't know if they will say the same if you go with the 4 bike add-on version. You have to call them to see. And they are pretty expensive.
Plan on likely having to also get an extension for the receiver, so the bikes don't hit the rear of the trailer. And "anti-rattle" clamps for the extension, to stop any wiggle due to slop in the receiver and extension. The rack and bikes move up and down a lot without them!
The wonder is why no one markets one? While maybe not a gigantic market, but the demand is certainly there!
2012 Ford F-150 Eco, Max/Max
Jayco 26.5 RLS, Reese Sidewinder