I believe all those parameter files have their own name. Since you have 1 mapping with multiple parameters files, and you want to start at once!
I would suggest to go with Runajobcli utility.
In this case you need to understand that is that possible to run 1 mapping those many times as per parameter files!
try merging all the parameters into a single file in pre-processing and use merged file as parameter file (have to test this, not sure). there is no way to specify multiple parameter file