The conversion of any building into a dwelling or the conversion of any dwelling so as to accommodate an increased number of dwelling units or families, shall be permitted only within a district in which a new building for similar occupancy would be permitted under this chapter and only when the resulting occupancy will comply with the requirements governing new construction in such district, with respect to minimum lot size, lot area per dwelling unit, percentage of lot coverage, dimensions of yards and other open spaces, and off-street parking. Each conversion shall be subject also to such further requirements as may be specified hereinafter with the subchapter applying to such district.