GP2.2 says "Plan the Process" and I’ve been trying to find out, to no avail, do we need separate plans for: Integrated Project Management (IPM), Technical Solution (TS), and product Integration (PI)?
The intent of GP2.2 is not to have a separate plan for each process, but to account for the tasks and deliverable of the process within your integrated plan. This is the best way to institutionalize the process is to plan for it, monitor that plan, and take corrective action when something does not adhere to the plan.
If you take REQM as an example, wouldn't you plan for eliciting their needs, reviewing the requirements, performing validation, updating traceability, and all of the other practices? In a way, the plan DRIVES the process, so it's pretty important.
So, no, you don't need a separate plan for each PA, but your plans do need to contemplate important process steps, and that's covered in IPM.