I was there when the leaders of one shul asked R Eliezer Melamed (Rosh Yeshiva of Har Bracha and author of the very popular Peninei Halacha series of halacha books) whether they could change the nusach of their shul, something that was desired by some and opposed by others.
R Melamed answered that you could not change the nusach as long as at least one of the original congregants was there and opposed the change. It could only be done if all agreed or new congregants had replaced the original ones. See here for some related thoughts from R Melamed (although not directly addressing the same question).
R Gil Student here brings a similar view from R. Yerachmiel Fried, in his Yom Tov Sheini Ke-Hilkhaso (final chapter, par. 16)
A synagogue whose founders established its text as Nusach Ashkenaz
according to the agreement of a majority of members, and through the
years new members joined, even though the majority now wants to pray
in Nusach Sefard the synagogue may not change its text because there
are still many members who wish to continue praying Nusach Ashkenaz,
even though they are now the minority. The same applies in reverse. (1)
All this only applies if they want to change a prayer practice in a
way that contradicts their previous practice… But if they… only want
to add to previous practices… they may change with majority agreement. (2)
(1) See Mishnah Berurah 68:4 and Responsa Yaskil Avdi 7:8. This also
applies to a private synagogue; see Responsa Zikhron Yehudah no. 46;
and see Pischei Teshuvah, Orach Chaim regarding a synagogue with no
(2) See Iggeros Moshe, Orach Chaim vol. 2 no. 21. And see Bi’ur Halakhah
468 sv. ve-chumrei ha-makom; Responsa Maharshdam, Orach Chaim no. 35;
Chelkas Ya’akov, Orach Chaim no. 79 regarding a synagogue built by a
donor on condition it prays a specific “format”, under what conditions
may it change. And also see on these matter Mishnas Yosef (by R.
Lieberman), Hilkhos Beis Ha-Kenesses.
See also here from Eretz Chemda.