The USNA Sponsor program is a two-sided deal. Matches are made randomly, with respect to criteria indicated by both sponsor family and plebe.
Sponsor families can request a specific incoming plebe. Plebes must also indicate on their paperwork they request that family. If the plebe doesn't request them, it's not supposed to happen, the "system" won't make the match. I don't know what the current plebe sponsor request paperwork looks like, if what I think you're asking is if there is a way for two incoming plebes to request the same sponsor. If there's a space to write it in, write it in! Never hurts to ask.
There are frequent informal "adoptions," where it just seems to work out better with one family than another. The plebe can then go to the Sponsor Coordinator and get the sponsor family name changed out. It's mostly just a formality, but makes it official. If a plebe goes missing, the sponsor family of record may get called by USNA staff. Best to have reality reflected on the record.
Our sponsor mids are always free to bring a friend. By the end of four years, out of any original crop of assigned plebes, we will have at least 1-3 adopted ones.