I have never considered such a dynamic for the Doctor, the family arguments would get very strange
They're both very strong, intelligent, and adventurous women who in their own way could handle the Doctor without completely dominating him.
What makes the dynamic interesting is that each has a different relationship with him, one as a lover and lifemate, and the other as a child and possibly a student.
Each also wants something different, River wanting a husbands love and protection, and Jenny wanting a father's approval. And both want adventure.
It would make a nice saga. Perhaps nothing as long term as a season, but...oh too late...was gonna say instead of no real companions during the sepcials maybe River and Jenny for all five. Nevermind that.
What would be very interesting would be that River isn't Jenny's mom, nor Jenny River's daughter, and their relationship would not be parent and child, but more likely a rivalry for the Doctor's attention, often butting heads abotu the right way to do things, etc.
What would be heartbreaking would be when we got close to when River was going to head to the library, the Doctor knowing but never able to tell. And then after River is gone, possibly forever "dead", talking with Jenny about love and loss.