From our MP's office:
As far as I’ve learned, IRCC usually follows a step by step process for their checks, but it isn’t always as such. If some checks require utilising a third party or can happen concurrently while other checks are being done, often we see several of those milestones ‘in process’ at the same time (Ex. Background and eligibility and criminality). We trust IRCC’s agents understand rules and procedures intensively and take those steps as they can. So no, there isn’t always a seeming logic behind the steps they take.
IRCC sets out urgent parameters for certain types of applications. But PR applications generally cannot be expedited. IRCC tells me that many of their internal checks and balances need to take place and they can’t be expedited (ex. Consulting with CSIS, CSIS has not obligation to process anything quickly, ex. Verifying a part of a travel history with another country, that country has no obligation to move more quickly).
You can always update the processing office, if circumstances have changed or anyone involved in the file is facing a dire situation. It doesn’t often correlate to a quick process, but it ensures the agent is aware. You can do so via the webform or via our office. When we check again in July, I could send something along if you’d like.