No limit. Typically your first day always starts as shortcall. Apart from that all lines are awarded as long call or known flying.
As a piece of advice, do not come to an ACMI expecting lines and known schedules. The company owns you for 16-18 days a month... just plan on that. Apart from 117 and very limited language in our contract do not expect any sort of scheduling system or practices like you may have seen at a regional.
Note: Omni is much better than other ACMIs at having you fly the known flying you are awarded.