I did eQip in November for DHS and FDA today. Both SF85P... DHS won't let you start working until fully complete but EPA will.
You will not have to SF 86 investigations open. Your new one can bump the other one out and you start fresh. Best to let the first one complete. Or withdraw from the position and start over.
The position designation is the key, either moderate or high risk public trust. If they are both the same then OPM will not initiate a new investigation when one is already in progress. However, the security office submitting your EQIP should be checking to see if an investigation has already been completed or is in progress that meets their requirement. Best thing to do is figure out what job you want and tell the other one to cancel their EQIP.
I really want FDA because it is actual federal government and the other is contract with DHS. DHS is supposed to only be suitabiliturgy yet I had to do SF85P. FDA is Moderate public trust.
Will FDA notify me of a pending investignition and ask me to cancel it?
You should ask your security liaison there.