Is there a general approach for designing a Trimmable Horizontal Stabilizer?
You always look at both in combination.

The first step is to use tail volumes that have worked before. This is enough for preliminary design.

When the design advances further, you have load cases to cover which combine trim and manoeuvring demands and you use trim settings and elevator deflections in combination. The useable deflection range changes with trim settings, because when the tailplane needs to produce a sizeable downforce to trim deflected fowler flaps on the wing, it cannot tolerate the same positive elevator deflection as in straight flight with lightly loaded tailplane.

Also, speed, load factor and loading determine the downwash angle on the tail. The useable stabilizer range varies with the downwash angle, so each load case needs to be looked at by itself.

Next, you pick the tailplane size and deflection range which covers all load cases and verify the result in the wind tunnel and flight test.