Experimental non-binary HRT

Hormone replacement therapy (HRT) is usually presented as a binary, MTF or FTM, and non-binary people seeking hormonal transition are warned of the all-or-nothing effects of sex hormones. But with a little creativity, it may be possible to tailor a hormone regimen towards the changes you want while preserving others -- or even obtain a hormone-free(-as-much-as-possible) body, via blockers and/or surgery removing one or more hormone-producing gonad.

This is almost totally uncharted territory! Most of the info I have on tamoxifen, for instance, is a handful of rumors from bodybuilders using it to prevent gynecomastia while on 'roids, and from a couple trans people who wanted to keep a flat chest. However, more and more people are forging their own paths (shameless plug from an anastrazole user, epochryphal).

Sex-hormone antagonists alone
If you identify as agender or genderqueer etc. (AMAB), or you want to stick to the reversible stuff, you may not want the "feminizing" effects of estrogen but still want to wash out testosterone. Many people elect to take only anti-androgens such as Spironolactone and Finasteride, without adding Estrogen or Progesterone into the mix. GnRH agonists/antagonists are an alternative, and may confer some advantages, but they're quite expensive.

Likewise, if you identify as agender or genderqueer etc. (AFAB), or you want to stick to the reversible stuff there too, you could use GnRH agonists/antagonists to prevent the ovaries from releasing as much estrogen/progesterone. This should halt the menstrual cycle and bring sex hormones to pre-pubertal levels, simulating the onset of menopause.

(AFAB continued) There are also aromatase inhibitors like anastrazole, and anti-estrogens like tamoxifen, and collectively these are all called "estrogen blockers." Anastrazole is usually prescribed for post-cancer patients to prevent its recurrence, but it has been prescribed to at least one non-binary person via the Center for Excellence in Transgender Health (which actually just runs through the UCSF Women's Clinic, so be aware of that). Again, at a high enough dose it should theoretically simulate menopause entirely.

However, having some amount of a sex hormone (either estrogen or androgen) is usually considered necessary to maintain bone health in the long term. This is not well researched! There have been eunuchs and menopausal persons for all of existence...but their age and health has not been much documented. Most doctors will not be on board to block all your hormones out of concern for osteoporosis, which is hard to prevent even with bone-strengthening meds if your hormones are minimalized. In this case, you could consider a SERM like Tamoxifen (whether you're AMAB or AFAB), since it will provide your bones with the sex hormone they need to grow and stay healthy, but without changing breast and other tissue.

Selective Estrogen Receptor Modulators (MTX)

 * Tamoxifen is a selective estrogen receptor modulator (SERM). In some tissues such as the brain it activates estrogen receptors, which may help reduce dysphoria. In breast tissue it antagonizes estrogen receptors, preventing the formation of breast tissue if desired.
 * Tamoxifen may also be taken alongside 17β-estradiol, more research is needed. In this combination, estradiol should still have its effects (combating dysphoria in the brain, redistribution of body fat, smoother skin etc.) while tamoxifen prevents the growth of breast tissue.

The wikipedia article on SERM mechanism is a good read, because it shows how extraordinarily complex these drugs are to cause estrogenic effects in some tissues but not others. This may also holp us understand the theory behind SARMs, though I don't know if they're phylogenetically related.

Selective Androgen Receptor Modulators (FTX)
Like their SERM sisters, Selective Androgen Receptor Modulators are an investigational class of drugs which try to modulate the androgen receptor differently in different tissues. SARMs are one of the holy grails of the bodybuilding community, which seeks to develop pure anabolic steroids to put on muscle while not having any androgenic activity (acne, 'roid rage, etc.) This is nearly a totally new area, and definitely falls into the category of mad science.
 * Enobosarm is apparently an anabolic but non-androgenic SARM under clinical investigation. Though not officially released, several athletes have tested positive for the substance, suggesting that it's availble somewhere.
 * While totally uncharted territory, SARMs could potentially be used alongside SERMs or even pure estrogen, and not interfere with each other since the anabolic effects of the Androgen Receptor are separate from the androgenic effects that reduce response to estradiol. This is very sketchy though.

Bodily feminization, mental virilization/feminization/as needed
Both estrogen and testosterone may cause changes in the brain (see neurosteroids for more information.) If you don't want your brain to change, just your body, or if you want the best of both worlds, there may be a way to keep the sex hormone balance of the brain different from the balance in the rest of the body.

The Blood-brain barrier (BBB) prevents many molecules, including common drugs, from entering the brain. Bicalutamide cannot cross the BBB, while her sister enzalutamide can (where she causes anxiety and seizures on occasion!)

Complete blockade of E/P from brain while retaining bodily feminization

 * Start bicalutamide, which prevents virilization of the body while keeping T levels relatively constant. Since bicalutamide doesn't enter the brain, the androgen receptors there will still receive and act on the circulating testosterone.
 * Use a non-steroidal estrogen such as diethylstilbestrol] which doesn't cross the blood brain barrier, to act as the estrogen to cause feminization. Alternatively, tamoxifen or another SERM can be used here (though tamoxifen crosses the BBB.)
 * Use an aromatase inhibitor to prevent the conversion of bodily testosterone into estradiol (which would cross the BBB.)

Estrogen + Progesterone + Testosterone in the brain, while retaining bodily feminization

 * Bicalutamide, as above, will prevent the androgen receptor from acting peripherally, but not in the central nervous system.
 * A higher-than usual amount of estradiol will already be present, since the all the unbound peripheral testosterone will be converted by aromatase into large quantities of estradiol.
 * If maintaining current testosterone levels is desired, a synthetic estrogen along with a synthetic progestin should be used. Natural estradiol and progesterone will inhibit the pituitary gland's production of FSH and LH, which will reduce testosterone production.
 * Testosterone may be centrally injected if necessary! It will only affect the brain, since bicalutamide is at work.

Research Wishlist

 * Investigate bodybuilding sites for discussion of SARMs.
 * Research the role of cofactors in SERM/SARM mechanisms of action.