LH and FSH are both released from the pituitary to stimulate testosterone release in the testicles. One knows that increasing LH and FSH can lead to further increase in testosterone, and furthermore testosterone has a negative feedback on LH and FSH, or does it?

Actually, testosterone has no direct negative feedback on FSH release. Only thru its aromatization to estradiol does this take place. One can thus assume that taking exogenous testosterone with an aromatase inhibitor can prevent FSH release.

T exerts both direct and indirect feedback on LH secretion, whereas its effects on FSH appear to be mediated largely by aromatization to E2.
If the hypothesis is correct that T has no direct negative feedback effects on FSH, it follows that administration of T in conjunction with an aromatase inhibitor or administration of nonaromatizable androgens should not inhibit FSH secretion. Previous studies from our group indicate that addition of the aromatase inhibitor, testolactone, abolished the 40% suppression of FSH observed when T was infused to normal men (12). However, the use of testolactone makes this study difficult to interpret given the knowledge that this agent has antiandrogenic properties due to its ability to bind to the androgen receptor (50). Administration of nonaromatizable androgens, such as DHT or fluoxymesterone, has been shown to have no impact on FSH secretion (8, 15, 51, 52, 53, 54) except at very high doses (55, 56, 57).
Unfortunately testosterone, and all the androgenic -anabolic steroids , do have a direct negative feedback on LH release.

1) Frances J. Hayes, Suzzunne DeCruz, Stephanie B. Seminara, Paul A. Boepple and William F. Crowley, Jr. Differential Regulation of Gonadotropin Secretion by Testosterone in the Human Male: Absence of a Negative Feedback Effect of Testosterone on Follicle-Stimulating Hormone Secretion1 The Journal of Clinical Endocrinology & Metabolism Vol. 86, No. 1 53-58