I got to think it will happen at some point because it happens to ever tv character. I'm not sure if they have a established character as of yet that it makes sense though I wonder about Harry Mudd though I doubt it. I mean he is already established as a loving husband.
Only 2 that makes sense to me is Lorca and TIlly. Lorca if they want to show her go to the dark side but I think Lorca and Cylon security woman might be a couple so that sounds to soap opera. Tilly also would be a dark side moment in that she is taken advantage of someone who looks up to her more as a mentor though it could also be a wake up moment were she realizes that she has gone to far and wants to change.
The other option and maybe my favorite is that she simply has casual sexual encounters. It's already been done with Kirk and RIker and early Bashir so it's basically a Trek tradition at this point. The difference is with those mentioned 3 the sex and romance I think was treated more like a fun hobby. Burnham being raised on Vulcan I don't think would consider sex or romance like that so instead it could be a byproduct of her ongoing depression from the events of the pilot.
Jason

Only 2 that makes sense to me is Lorca and TIlly. Lorca if they want to show her go to the dark side but I think Lorca and Cylon security woman might be a couple so that sounds to soap opera. Tilly also would be a dark side moment in that she is taken advantage of someone who looks up to her more as a mentor though it could also be a wake up moment were she realizes that she has gone to far and wants to change.
The other option and maybe my favorite is that she simply has casual sexual encounters. It's already been done with Kirk and RIker and early Bashir so it's basically a Trek tradition at this point. The difference is with those mentioned 3 the sex and romance I think was treated more like a fun hobby. Burnham being raised on Vulcan I don't think would consider sex or romance like that so instead it could be a byproduct of her ongoing depression from the events of the pilot.
Jason