[1] "Mike went to the theater early so that he could find a seat".
[2] "Mike went to the theater early so that he found (*find) a seat".
If, as in [1], you include "could", (whose meaning here is 'potential ability') the subordinate clause is clearly a purpose adjunct. We understand that the purpose of Mike going to the theatre early was to give him a better chance of finding a seat.
But if you omit "could", as in [2], the meaning is different. This time it becomes a 'result' adjunct meaning that Mike went to the theatre early and as a result he found a seat. This meaning differs from the 'purpose' one in that it implies that Mike did actually find a seat, whereas in [1] Mike's finding a seat is only a possibility.
I'd say that [1] is the salient interpretation, so "could" should not be omitted.