If you have shell access, check out man quota.

Update: In a past life, fraught with student users who thought Unix was spelled with an 'E', I enforced some pretty harsh quotas for new accounts. These were, however, relaxed into a larger pool for the asking, and could even be expanded to some pretty extreme values with a faculty sponsor (for research or the like). I would typically not refuse requests into the larger pools (my job was to support the education), and automation (quite a bit with Perl, IIRC) made applying these quota pools very easy and flexible. They were set up to avoid non-terminating loops from filling the user file systems, and keep the student Unix network more reliable.

Assuming that quotas are in place, talk to your vendor. They may have a quota in place to help keep one customer from impacting another (at least without giving the admins time to respond). If this is the case, they may not have a problem with either (1) raising your quota (perhaps for a price), or (2) you storing some select files in a filestore of some sort, for example, a ZIP, YAML, DBM::Deep, or some other type of file.

It may also be time to re-architect how you are storing your data files.