I don't think any TNG-era senior staff actually manages to make a straight (5 consecutive ranks) or a flush (5 officers in same color), actually.
TNG manages a full house (Cdr, Cdr, Lcdr, Lcdr, Lcdr).
DS9 never gets much of a hand, though it manages a straight at the end IF you include Kira and Nog (Capt., Lt. Col.*, Lcdr, Lt., Ltjg).
Voyager maxes at 2 pair (Lcdr, Lcdr, Ltjg, Ltjg). If you give Harry the rank he would have had if the showrunners had had any sense whatsoever, this adds a third Ltjg for a full house.
TOS... I'm not sure because I never figured out the insignia.
Enterprise... there seem to only be four ranks, so straights are impossible. Once T'Pol is given a Starfleet commission, they manage two pair (Cdr., Cdr., Ens., Ens.)
*When Kira is commissioned in Starfleet, she receives the rank of Commander. This suggests that her Bajoran rank is the equivalent.