Multi-level process development I was previously acquainted with a specific model, which contains levels for different phases of a systems development, ie: Phase 1: Complete chaos, nothing works Phase 2: Getting stuff to work, but breaks, no process Phase 3: Implement processes to stop things breaking Phase 4: Scale etc.. I think it had an acronym like MMCM or MMCP or such, but can't find it via Googling.

You appear to be looking for Capability Maturity Model Integration (CMMI). The CMMI Institute seems to be the organization currently behind it.