Clarification on Choosing Alliances

I have a question regarding the alliance choosing process, but it is easier to see with an example.

Lets say you have a tournament with 18 teams. When choosing alliances, the #1 ranked team chooses the #3 as their alliance partner, the #2 ask all teams and all decline except for #16. We only have 2 alliances, 6 more alliances to be formed, but we only have 2 more teams in the pool to choose from (#17 and #18). How do you solve this issue?

I ask cause this was an issue in one of the local competitions last year; and it is very likely to occur once again since teams are arriving to tournaments with pre-agreed alliances.