File a flight plan from point of departure, intermediate locations, to the final destination with remarks regarding the additional stops. If weather allows, you could cancel when close to each stop and let the controller know that you would like them to keep your filed flight plan in the system and you'll be reactivating it in approximately XX minutes.
You situation is very similar to how we conduct our operations when we take off from one location, have work to do in multiple locations enroute, and land at the final destination.

In the military we had something called a Stopover Flight Plan.
One flight plan filed with multiple IFR legs with delays built in (for stops).
I never like to do this personally. I took my time at each stop, checked weather again, checked in with Ops if required, and refiled the next leg. I'm not sure there is a FAA equivalent of a Stopover flight plan.

If the possibility of IMC conditions exist, I would call FSS and tell the specialist that I would like to file multiple flight plans at one time, giving the pertinent details of each before he closes out each flight plan. Then I would basically fly each as a separate leg with individual flight plans ready and waiting for me prior to departure.

Something about multiple ways to skin a cat rings to mind here
Good luck and thanks for contributing to Angel Flight.

USMCFLYR