Upvote:2
If you have multiple PNRs, it's possibly not a single booking, but two separate tickets. Better check directly with the airline to see if you can have your baggage checked through or if you absolutely must re-check it yourself.
According to the Roma Self Connect tool on the website of FCO, you'll have to go through immigration, collect and recheck your baggage and then go through Schengen exit again. For that you will likely need an ordinary Schengen visa (unless your nationality makes you eligible for visa-free entry).