The parent application was filed in 2019 based on a provisional filed in 2018. I didn’t fast track the parent, thus it is still pending, and it contained enough material for several patents. Since then I’ve filed 2 CIPs and a divisional, and will be filing a new CIP of one CIP where I need material from the parent that I deleted in the intervening CIPs. Can I do this and still keep the parent’s priority? And if I instead file this new application as a CIP directly on the parent, also incorporating new material from the intervening CIP, will that trip me up?
Since the content you need is in an application that is pending the new application can get the info directly, there is no intervening application. Just claim priority to the parent and forget the others.
If the patent was no longer pending but overlapped a currently pending application you could still reach back. It would take a wordier sentence claiming priority.
Regarding CIPs - they are not magic. On its face, CIP only has the priority date of its filing. If some prior art comes up that is dated before the filing it can be cited. The burden then is on you to establish that specific claims are fully supported in the application from which priority is claimed.