Networking for FT after Accepting SA

Hello All,

This past summer I received and accepted a SA spot for the Summer of 2020. I am content with it and excited to embark on that when the time comes. That being said I don't want to be left out in the dust in a situation where I do not receive an offer and might want to look at other opportunities if I do not enjoy the experience. That is why I want to network with others starting now for Full Time, as a safety net. It feels weird to do so because the community is small and I don't want the firm I already accepted an offer to think I am just going to leave and start off the summer on a bad foot. How would you monkeys go about networking for a FT offer before you even started the summer stint? Should I even worry about networking for FT now? If I do network with individuals, what is my ask? For SA I was very direct and asked them if there were opportunities, can I do that for these guys even if I have something in my pocket? Thoughts?