Well -- according to one source, the GSR had 25 constituents; some generally reckoned "mad and nonsensical". Without outright cheating or attempts at same: I can come up with a -- probably not precise enough -- number in the mid-teens.
5' 3" gauge:
Great Southern & Western; Midland Great Western; Dublin & South-Eastern; City of Dublin Junction (doubtful -- reckoned to be, to all intents and purposes, part of the D&SE); Cork, Bandon & South Coast; Timoleague & Courtmacsherry; Cork & Macroom Direct; Waterford & Tramore. And I think there was a weird notionally-independent "joint-something" broad-gauge concern, involving Rosslare.
3' gauge:
Cork, Blackrock & Passage; Cork & Muskerry; Schull & Skibbereen; Tralee & Dingle; West Clare; Cavan & Leitrim.
And the hapless Listowel & Ballybunion Monorail, which was not brought into the GSR: as at mid-1924 it was still running, though physically and financially in a bad way -- those doing the sorting-out re the shortly-to-be-set-up GSR, refused to have any truck with something anyway so barmy, and basically in a state of ruination; it closed in October 1924. (One feels that this was rather unsporting and Scrooge-ish on the part of the embryonic GSR; can, however, see their point of view.)