Convert internship before starting

Hello! I am a final-year UK student in the following situation: I have an offer for a full-time position at a firm (smaller firm) and a (second) summer internship offer at a firm I like more (investment bank, with established SI-->FT pipeline). Both are conversions from past internships I did at these firms. I received and accepted the internship offer before receiving the other FT offer, to which I still haven't replied. Now, my question is: could I somehow leverage the FT offer to convert the SI offer directly to FT before starting the internship, so that I would start directly on the graduate scheme? Even though I like the bigger firm more, I wouldn't want to risk losing an FT offer on a SI which may not convert and then be left unemployed.