The phrase "full caseload" means having a lot of work or responsibilities to handle. It is often used to describe situations when someone has a large number of cases or tasks to manage. Full definition
All of the solo attorneys I know with full caseloads have actual offices. (lawyerist.com)
Postdoctoral fellows will carry a full caseload of 3 - 10 individual psychotherapy cases, conduct psychiatric intakes, potentially start and / or co-lead one outpatient therapy group, and opportunities to participate in dyadic and family / couples treatment in the outpatient program. (themotherhoodcenter.com)
and another to do it with a full caseload, but it is a lawyer's duty to prepare adequately, if not better. (lawyerist.com)