You have to deal wth the most imminent threat 1st......and thats the depress 1st.
I had this recently in the sim and although our company provides no specific guidance (its impossible to legislate for every possible senario) it was quite obvious that we were unable to comply with Climb RAs.
*If we reacted to the "climb" RA we would actually increase our chance of collision as our pull-out from the dive is limited to 2.5g......ie: 3-4,000ft
1. The extra high RoD meant that they were many more 'threats' and consequently RAs. It was disconcerting!!
2. We tended to get an RA "Climb" and then the very next second it changed to an RA "Descend".
I dont know (and cant find) of any software within the TCAS that takes account of aircraft with significantly high RoDs but we certainly noted that the TCAS very quickly changed its mind due to our vertical profile.
I hope someone with specific TCAS knowledge can join this thread.
On you next sim, ask to see this in action. Its well worth it!