Not necessarily as romance, flings, or something and in no order: Meredith Stout (provided you sided with her), Rita Wheeler (Mox bouncer girl) and the other bouncer girl, Lizzy Wizzy (if she got rid of her BF at the end of her mission), Rogue (if she's still alive), Sandra Dorsett. There are probably more that I don't remember right now and probably several male characters like Vic.
I've said it to death but remove the body type restriction on River's romance so gay players have a less controversial option who already has voiced content. And then just more content for both existing male romances, who are massively lacking in content compared to Panam and Judy. Also (and this goes for all romances but again, much more needed for the males) more interactions and texts where they ask about you and how you are doing. V is DYING. He/She is terminally ill in this horrifying, existential way and Kerry doesn't seem to care much at all and River seems oblivious to your condition and to the whole main quest in general (compare it to Judy where you can call her and update her after the parade mission, for example). We want to get to know these characters but we also don't want them to speak at us. It's as lame in game as it is in real life. Let us roleplay our motivations, backstories and reactions to in-game events with the romance characters as a device for that.
As for adding more options, I don't want to speak for anyone else (though Misty seems a great candidate for people into women building off your rapport in the base game?) but I'd be very happy with just fully bi River. Other options are Saul (!!!) and Takemura, as attractive male characters already integrated into the main plot.
I feel like Misty is the best pick for people into women for FUTURE content, but all post-first game. Her and V have a nice connection but it makes sense that for a while she's still getting over Jackie and it would make it a nice slowburn romance if she is an option later down the line.