[AZ-AlphaXi]

Under the "Membership Recruitment Mechanics" section the
"green" book says

Each fraternity is entitled to pledge the full Quota at any time during the year even if by so doing, the allowable Total chapter size is exceeded and the formal membership recruitment period is over.

Once established, Quota should not be changed until the next formal membership recruitment period when a new Quota will be set.


So the answer is no, there should be no time limit on when a chapter can take up to quota.