I see references to an upgrade between 7.3.2 and 7.4.x but don’t see it available on the https://suitecrm.com/download website. Today’s date 1/19/2016
I do see a few references to difficulties when this was running.
What is the current upgrade path beyond 7.3.2
I believe the current upgrade path from 7.3.2 would be
7.3.2 > 7.4.3 via the upgrade package called “SuiteCRM-Upgrade-7.3.x-to-7.4.3”
7.4.3 > 7.5.3 via the upgrade package called “SuiteCRM-Upgrade-7.4.x-to-7.5.3”
Both packages can be found on the download page here; https://suitecrm.com/download
I would recommend doing a Database and CRM backup before upgrading, just in case.
After each upgrade, I would recommend ensuring that your permissions are appropriate for your instance, and it may be a good idea to run a few Quick Repair and Rebuilds and Execute any changes if given the option.