Very simple suggestion, and I think would be easy to implement.
Have 2 different sets of weekly boosted players, one for PVP and one PVE. That way, those who want to play both can make better use of their squad and save some Health Packs.
This would help a lot of players in their 2* to 3* transition (like me), and wouldn’t change a bit for everyone into 3* and 4* land. I guess for those guys it would maybe encourage them to play a little more PVE. Imagine Iron Fist and Luke Cage are boosted on PVP, but say Patches and Loki are boosted on PVE. People may be willing to play just for the sake of changing a little bit.
I’ll explain: I grinded heavily at the end of Heart of Darkness event, using mostly Ares and OBW since they were my highest leveled characters. But when the event ended, Ares and OBW would still be my best team to play on the Captain Marvel PVP event. If I had for instance Thor and Storm (or rather any other 2* boosted chars) I could have won a few extra points and it would have helped me a lot (since I used all my health packs on hearth of darkness).
thanks!