The client found that there was an ACS routine that has been assigning their View and Deliver database extents to a DATACLAS that has a DYNVOL of 32 - enabling each extent to expand 32 times. With that, each database extent is allocated 32 entries in the TIOT table, which are not used, but were filling up the table.
The client will have the ACS routine altered, so that the View and Deliver database extents are designated to another data class, so as to not have TIOT table entries allocated.