Carryon plus small daypack

You can take them both. I have an Osprey 46. I don't have the daypack (dont know what that is), but we routinely bring a stuff able daypack that we use to fill with weighty things so that our bags make weight, then we transfer the backpack things back into the Osprey once we're on board, if that makes sense. Point is, we carry a day pack and Osprey on

What airline are you using?

Andrea brings up a good point. The answer is heavily dependent on your airline. You will also find bigger allowances for international flights Vs inter-European flights.

Check all your airlines.

Many have a one bag only policy for Inter-European.

American to London, I don't know what airline from London to Rome.

There is a small Osprey daypack that attaches to the Porter, I figured I could take a few necessities in the daypack and detach it from the Porter and that would keep the Porter from getting to heavy.

Most airlines allow a 'personal item' as well as a carry on. Your small daypack would qualify as 'personal item' if these are the only 2 pieces of luggage you are carrying. But, as mentioned, it is all airline dependent. This is just one of several websites that list dimensions and whether personal item is allowed. https://travel-made-simple.com/carry-on-size-chart/
From there, go to the specific website for any personal item dimensions. If the daypack isn't stuffed full, it is malleable enough to squish into whatever size they list.
I do note, however, that the 46 dimensions are too big for most airlines in depth, so you will need to underpack or it won't fit into the airline 'compliant size' metal tester frame.

My only experience, so far, with inter-European air travel was on Easy Jet. I travel with a RS rolling carry on and a backpack as my personal bag. Easy Jet only allows one carry on, so when I booked my flight I paid extra to check my rolling bag. If you wait to pay at the airport it costs more.

I travel with an Osprey Porter 46, and that stuff-able daypack (made by SeatoSummit). I have traveled this way on Delta, United, Easy Jet, RyanAir, KLM, Lufthansa, Southwest, and American... So far so good. But as I said, we weigh our bags (our family of five all have the same bag set-up) and tighten straps so the dimensions/weight fit the airline's requirements

The daypack I am referring to is the Osprey daylite, what I like about it is that it attaches to the Porter and the cinch straps on the Porter go on the outside of the daylite. I have never used this setup on a flight yet, and that is my concern, I have traveled with carryon only for years and I am nervous about have to check the Porter 46.

I used the Osprey configuration you refer to on our trip to Italy on Delta. There were no issues with carry-on and I feel it's a great combination.

@Andrea — another trick you can do with EasyJet is pay for EasyBoarding — then they allow you to bring a personal item in addition to your carryon/rolling bag. Sometimes this works out cheaper (or more convenient).

Kim, thanks for the tip. That's good information to have.