similar to Monoprix?

Which city? There is Rinascente, which is a large chain. Also OVS, Eusospin, etc. Then there are others that sell also food, like Unicoop.

Does Conad count?
I am done. the query

I looked it up and it seems Conad is what I'm looking for!

Carolanne, we passed a Conad or two last month in Calabria.
I am done. the 'C's

Conad stores vary from closet size to hypermarkets. Ask a local

Conad, COOP, Pam, and Penny

I think you will find that there are stores that primarily do groceries and those that do sundries. Perhaps in the larger cities you may find a Conad or Coop that has some items that do not fall in the grocery category, but do not expect a vast selection.

There is also a chain called Tigota.
No food, but many toiletries and household things.
I’ve seen the shops in many towns in Italy.
Conad is a grocery store.

There are a lot more supermarket chains in Italy than the names mentioned in previous comments. Some are regional (such as Cadoro in the Veneto), others are everywhere. If I think of the one Target in the USA that I have ever been to, I would say IperCoop, Carrefour or Auchan are similar.

Without knowing in which regions you will be, it is difficult to give very specific answers. It also depends if you are more interested in food or non-food.