The National Institutes of Health (NIH) Grants Policy Statement on Stipend Supplementation, Compensation, and Other Income 
provides guidance on Trainees seeking part-time employment outside of their full-time training appointment.
Keep in mind, T32 awards are for full time training activities therefore 100% of stipend, health insurance, tuition, and fees should be charged to the T32 award. If the T32 cannot cover 100% of the tuition and fees a portion of the remaining costs to another institutional funding source may be allowable dependent on sponsor and institutional policies and as long as its consistent with the level of effort on that source.