A company has several shareholders, the majority of which are Jewish (about 60 – 65%). The business has shops open on Shabbos and Yom Tov although the public is unlikely to know of the Jewish ownership. Previously the business had a managing director who was not Jewish (and he was a 10% shareholder) and he insisted shops remain open on Shabbos / Yom Tov. There are new directors of the business (2 people) who own about 14% of the business. They are Shomer Shabbos. The one would close the business (or enter into a sale agreement) if majority his, and the other keeps Shabbos but it is unclear if this shareholder would close the business if his say. The majority shareholders would object strongly to closing the business on Shabbos. What should the Shomer Shabbos directors do? Can they continue to run the business without leaving explicit instructions for Shabbos trading? Do they need to sell their shares over Shabbos? Is there anthing else relevant to consider?
They can continue to run the business as usual, and under the circumstances there is no need for further action.
Please see sources, below.
Where non-Jewish workers other than the non-Jewish partner are working on Shabbos, the matter of a partnership is lighter: see Magen Avraham 245:1 and Mishnah Berurah (1), and see Aruch Ha-Shulchan 245:11.
Where there are no non-Jewish workers, the Shulchan Aruch (245) requires a spitulation with the non-Jewish partner whereby the income for Shabbos goes to the non-Jew, and the corresponding income from another day is given to the Jewish partner. If the stipulation is made, it is permitted to eventually share the income in proportion with the share of the partnership.
The Rema, however, is more lenient, and cites from the Ran (21a) who rules that where the Jewish partner does not take on a specific day of the week corresponding to Shabbos, it is permitted to share the income of Shabbos (from the non-Jew’s work). This idea is ruled by the Sho’el U-Meishiv (1:3:55), and is relied on by a number of authorities (see Minchas Yitzchak 9:21; Shut Maharshag, Orach Chaim 45).
if the Jew is doing “extra work” in the weekdays, corresponding to his “taking Shabbos off,” the Rema is only lenient bedieved, and lechatchilah one must make the stipulation mentioned by the Shulchan Aruch.
In the case of the question, and provided that the workers for Shabbos are non-Jews, that (as noted in the question) the company is not renowned as being under Jewish ownership, and that the stores are outside Israel (so that the custom is predominantly non-Jewish) it is therefore permitted to continue to run the company on Shabbos.