They eventually did that plot on VOYAGER, with B'Elanna getting split into her human and Klingon halves.
Meanwhile, back to TOS . . ..
"Catspaw": Ditch DeSalle and let Uhura be in command while the rest of the bridge crew is stuck on the planet.
Having watched Balance of Terror yesterday, it looks like Uhura was in charge of the bridge as everyone else was in conference and if there had been a more senior officer of the watch, Kirk would have called them.
For me, I would just feature more women more often. I think Shore Leave was the only time we had two women chosen for a landing party (they otherwise just get kidnapped in pairs). Rand's contribution to Corbomite Manoeuvre and Balance of Terror were lamentable. Give the poor woman something worthwhile to do! In Enemy Within, I would have Rand be the one to find good Kirk unconscious in sick bay so she doesn't look so dumb. I would have liked to see Harlan Ellison's more adventurous version of Rand. Plus Rand in CotEoF, Space Seed, a Taste of Armageddon, The Galileo 7, Operation Annihilate, Return of the Archons, this Side of Paradise, I, Mudd, the Trouble with Tribbles, the Tholian Web, a Piece of the Action, Spectre of the Gun, and Turnabout Intruder.
More John Colicos for sure. He had a lot of charm and personality. I'm not sure I'd want him to replace all the other Klingons since that would have robbed us of the three amigos in DS9 but find a way to get him in somehow. Same for Miranda Jones. More Orion pirates too.
More Uhura working on cryptography instead of Spock. More Chapel taking the lead on medical research with McCoy assisting her. Helen Noel in Whom Gods Destroy. Riley in Catspaw and Piece of the Action plus a better wig for Chekov in his early episodes. Carolyn Palamis in the Apple and Friday's Child.
A line about atmospherics in the Enemy within. Photon torpedoes in the Balance of Terror plus limited warp engines for the Romulans. Say Uhura's synaptic connections have been scrambled rather than a mind wipe. It's just silly to say she could be re-educated to be a bridge officer after that.