Section 7. A mutual holding company organized under this chapter may:
(1) invest in the stock of one or more banking institutions as defined in section one of chapter one hundred and sixty-seven A;
(2) acquire a mutual banking institution through consolidation or merger of such institution with its subsidiary banking institution;
(3) merge with or acquire another holding company provided that any such holding company has, as one of its subsidiaries, a subsidiary banking institution;
(4) invest in a corporation, the purchase of the capital stock of which is permitted for a banking institution under state law;
(5) exercise any other power or engage in any activity permitted to a mutual banking institution chartered by the commonwealth;
(6) engage directly or indirectly only in such activities as are now or may hereafter be proper activities for bank holding companies under chapter one hundred and sixty-seven A or by applicable federal law or regulations; and
(7) exercise any rights, waive any rights or take or waive any other action with respect to any securities of any subsidiary banking institution which are held by such mutual holding company.