We have terminated a 24 fiber in a junction (30"x24"x8") and have several 1-2 fiber coming out to various points. The would like to use this box to pull additional multi-fiber through the same box. I believe this is not allowed. I need clarification.

Sounds like a specification or design standard if it is not allowed.

There is nothing not allowing this to be done in the National Electric Code Article 770 Optical Fiber Cables and Raceways.

You can review this at NFPA 70: National Electrical Code®

You may need to check with the standards that cover the installation of optical cable, TIA-EIA see:
TIA/EIA Structured Cabling Standards on line - Google Search