Hotel for family of 4 but most places list 3

You might try Incentrum. It's apartments in a couple of buildings, but operated through a central office, like a hotel. I see they have some options for 4 people.

https://incentrum.it/en/home-page/

We stayed at one of their suites on Via Babuino there in November 2021, and the location was excellent (close to the Spanish Steps) and the apartment spacious and comfortable.

Try searching on booking.com. You can enter 2 adults and 2 kids and it will show you rooms that accommodate 4.

If you need a room that will sleep two adults and 2 children use booking.com to filter for your # and the kids’ ages. We have also emailed smaller hotels that tend to have a variety of sized rooms (unlike known, chain brands) and sometimes even an annex/apartment they rent if you tell them your group makeup. We’ve booked many triples and some quads over the years in Rome and many European cities. You should mention a quad or family room for 4 and tell them the kids’ ages if you email.

Last year, we needed a room for 5 in Rome. As this, a/c and an elevator for a bum knee were our determining factors, we stayed at the Hotel Globus (a Best Western hotel) on Via Ippocrate. It is between Roma Termini and Tibertuna, and not near the big touristy things like the Coliseum, the Vatican, or Pantheon. However, we found it very easy to get around via public transportation and taxi, and a very comfortable hotel.

Ask for a family room. In Europe most places charge per person including children rather than per room as is common in the US.

I just finished booking some hotels in Italy for our son’s family, as they will join us on our next trip. I used booking.com to identify places with space for 2 adults and 2 11-year-old children, then went to the individual websites to do the actual booking. In many cases, the rooms offered had one double or queen bed plus a sofa bed, so the kids have to share. There were a few with 3 beds, a double/queen and two twin beds.

As Frank said, the booking is for a specific number of people, and prices are based on that (sometimes with a reduction for children). A room with 3 beds may be a triple (3 single beds) or a quad ( one double/queen and 2 singles). so you have to check the intended capacity.

We usually get two rooms for this reason. If you’re a Hilton person, they have guaranteed connecting rooms.

My mom, my husband, and I are going to Italy in September. I wanted to have separate rooms for Mom and for my husband and I, so I chose this time to book through AirBnB and VRBO. There are a multitude of choices going that route! I opted for apartments that had clothes washers, an elevator if it wasn’t on the ground floor, and was able to choose a lot better where exactly in each city that I want it to be. The cost to utilize one of these options is pretty much, the same as what it would be to book a room for several people. I would look into that!
Be sure to read reviews for each option because you may find other people who have stayed in that unit before you have negative reviews that are valid, or very positive reviews. That was one of my criteria for sure, was to check the reviews before moving forward. Be sure to look for ease of checking in, cleanliness, ease of contacting the owner, if necessary, etc.

Hotel rooms in Europe are typically just designed for two people. Our family of four usually just gets two rooms or we rent an Airbnb. If you are lucky you will find a family room using proper filters on booking.com.

Look at staying in a convent/monastery ! Something unique ! Most have quad rooms. www.monasterystays.com

I agree with the convent idea. In 2008, We enjoyed our stay near the Colosseum, I think Il Rosario.

Thank you all for your input! We checked out all the options and ended up picking an Airbnb.