Parma/Modena for 3 days Question?

I have not been to Parma or Modena, so unable to comment on whether there is enough to do if you home-base it there for 3 days. (And, is that 4 nights, meaning 3 full days, or do you mean 3 nights, which is only 2 full days?) We stayed in Bologna for 5 days (6 nights) many years ago at the end of our Italy trip, and found that to be a good amount of time. However, we did not do any day trips. (And, oh how I regret not going to Ravenna to see the mosaics when it would have been feasible to do that!) Your longer stay in Bologna would allow you to do that, plus also go to Modena for the day (looks like it's a 30-min train ride). If you really want a second home base in Emilia Romagna, perhaps Parma would make more sense than Modena. Parma might be feasible as a day trip from Bologna, just a bit farther than Modena. Just depends what you'd like to do there and whether a day trip will allow adequate time for that. I'm assuming you'll be doing all of this by train (or occasional bus).

I'm unsure if you've been to Rome or Venice before, but having been to both of those cities, I would suggest you add more time to each if possible, even for a return visit. I would add more time to those places that are already on your itinerary rather than add more to the list, i.e., I would save Florence and Lucca for another trip where you can focus on Tuscany.

I'm guessing you have a reason for booking RT flights to/from Roma. (Perhaps you can get non-stop flights; if so, lucky you!) Another option -- if you haven't yet booked your flights -- is to fly open jaw ("multi city") into one and out of another, rather than backtrack to Rome for only one day. We flew out of Bologna (BLQ) to Munich via Lufthansa, then home, and found that small-scale airport to be so easy to navigate. It would make more sense to fly into Venice for xxx days, train to Bologna, see other parts of Emilia Romagna, then train to Rome for xxx days, and fly home from there.

Here's a post today re: Italy itinerary planning. There's some good advice here that you might find helpful, especially re: not moving around too much and why flying open-jaw may be more efficient:
https://community.ricksteves.com/travel-forum/italy/help-with-itinerary-23e4ec9c-f420-4fab-ade5-48491f848f41

You can easily day trip from Bologna to both Parma and Modena. I personally wouldn't spend more than a day trip in Modena. Both are easy train rides from Bologna. Also nearby are Ferrara and Ravenna. I love Ravenna and take most visitors there and we spend the night. Another nice small town is Arezzo which isn't far from Florence and again I would spend the night because it is a beautiful small town where you can get a good feel for the local life. I think it depends on what you want... I can always spend another day in Rome (and I've spent weeks there) and the same with Florence since I visit both cities at least once a year. There are many small towns on the train line from Bologna to Modena on to Piacenza that have quaint historic centers and great food. That area is part of the pilgrimage of the Via Francigena.