Muldrake
Not really enough information is provided to answer the question, but assuming you have TCAS version 7 (which improved multi aircraft encounters), I would have expected the scenario to run:
Initial Descend RA during or after which time the second aircraft would have been "trafficked", then as the second aircraft threatens an RA your own RA should be adjust vertical speed (no descent) to prevent descent onto the second aircraft or if insufficent separation exists a Climb RA as you say. If the second aircraft is Mode S equipped it should have received a coordinating maneouvre to descend, if its Mode C or no TCAS then your own Climb RA is more likely. Similar situation for the third aircraft.
Given the rough FL's, headings and distances you could run this through a TCAS simulator to evaluate the responses.
If you descend slightly too much you will most likely get the climb RA for the second aircraft, if you don't descend enough (perhaps because you are aware of the second aircrafts position) you will likely get an Adjust Vertical Speed (no descent) part way through the descent, if you descend like a rock then you may get an Increase descent or descend crossing descend to cross the second aircraft flightpath, in which case the third aircraft is probably no factor. If you time it just right you may get a Monitor Vertical Speed with (no descend) for 2nd aircraft and (no climb) for 3rd aircraft. In which case you are the filling in an aluminium sandwich
