gh downregulates the production of t-3--ideally you would add just enough to make-up for the down reg--but it is hard to know how much to use.
"What may not be an effective strategy to maintain muscle mass during a T3 cycle is the use of exogenous growth hormone (GH). Studies have shown that when GH and T3 are administered concurrently, the increased nitrogen retention normally associated with GH use is abolished. This has been attributed to the observation that T3 increases levels of insulin like growth factor binding protein, reducing the bioavailability of igf-1 (14). Nevertheless, GH has fat burning properties independent of igf-1, so using GH with T3 would act additively to speed fat burning, but with little if any preservation of lean body mass. So again, if GH is used in conjunction with T3, anabolic steroid/prohormone use would be indicated"
Thyroid Hormone for Weight Loss:
Physiologic and Metabolic Effects
by Karl Hoffman