We are just not sure how to automate running the proc for each group for each process code...
There's more than one way that this might be done, but one which should definitely work is this:
1) Create a physical 'work' table which will hold the results that the proc outputs.
2) Modify your existing proc to append its results to this table.
3) Create a 'master' proc which does the following:
a) Truncate the work table.
b) Loop round all group-process combinations and call the child proc for each.
Your SSIS package now takes the work table as its input ...
Perhaps even better would be to modify your proc to do all of the work in one shot, but maybe that's too complex to code/handle - I'm in no position to assess that. But I did study to be an actuary years ago and know that nothing is simple in that field.
If you haven't even tried to resolve your issue, please don't expect the hard-working volunteers here to waste their time providing links to answers which you could easily have found yourself.