Hmm could be an assumption, especially becauses E3 antagonizes E2 when it's not present in a continuous fashion.
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https://en.wikipedia.org/wiki/Estriol_(medication)
"
Although estriol is an estrogen, it has also been reported to have mixed agonist–antagonist or partial agonist activity at the ERs. On its own, it is said to be weakly estrogenic, but in the presence of estradiol, it has been found to be antiestrogenic. However, this is again due to the fact that estriol is a "short-acting" estrogen. If estriol is present continuously with estradiol, it shows no antagonism of estradiol. The co-administration of estriol with estradiol has been found not to influence the effects of the latter in women, including neither enhancing nor antagonizing the effects of estradiol."
From studies:
"Short acting estrogens would not be antagonists if they were present in a continuous fashion which would result in constant or long term occupancy of the estrogen receptor. Pollard and Martin showed that frequent administration of DMS stimulated full estrogenic responses in the mouse vagina. They suggested that this effect was the result of continuous occupancy of receptors, We confirmed these observations in the rat by injecting estriol every 3 h for 15 h and observing full estrogenic stimulation of the uterus. Likewise, Martin et al. obtained similar results with the mouse uterus. These results demonstrate that short acting estrogens are neither ineffectual nor antagonistic when present in a continuous or chronic fashion."
"Whereas estradiol remains bound to the ER for 6 to 24 hours with a single short-acting injection, estriol dissociates from the receptor much more rapidly and stays bound for only 1 to 6 hours. As a result, estriol can only induce estrogenic effects which require short-term interaction with the ERs. Induction of endometrial mitoses requires the ligand to remain bound for at least 9 to 12 hours, and this is thought to be responsible for the lack of endometrial proliferation with estriol in many studies. If estriol is delivered more continuously than a single administration per day however, for instance if it is given as a subcutaneous pellet, as a depot injection, or in multiple doses two or three times per day, this results in more sustained exposure to estriol and full estrogenic responses equivalent to those of estradiol occur."
"Unlike oestrone, oestriol cannot be converted to oestradiol. It acts as a weak oestrogen, because the duration of nuclear receptor binding is relatively short. It therefore has no proliferative effect on the endometrium when 2 or 4 mg are ingested. However, where the presence of oestriol in the target cells at sufficient concentrations is prolonged, e.g., when 4 mg is taken twice, or 2 mg 3 times per day, or high doses are ingested (8 mg or more daily), the hormonal action of oestriol is enhanced."
"When oestriol is administered together with oestradiol it does not exert any demonstrable biological effect, neither enhancing nor antagonizing the action of oestradiol"
I guess that there won't be a problem if it's taken alone and not surpass the normal levels, because is acting like estrogen, weak, but estrogen. Although, when it's come to E2, they should be taken together, like the researches mentioning. Otherwise, I think it would/will be bad for hair in general. (though->
The co-administration of estriol with estradiol has been found not to influence the effects of the latter in women, including neither enhancing nor antagonizing the effects of estradiol---So, I can't truly tell)