Verb that means "to be in a relationship with"?

I know you can say, I'm dating him or her. Is there a verb (an -ing verb in this case) that can be used like that but for being in a relationship (the further step)?

Example:

Sam's not exactly a gay man. He's a transgender. So technically Mark'll still be ___ing a woman.

I checked the synonyms of dating. Bus as I expected they all mean dating, not being in a relationship.

(Idioms are also welcomed.)

Solution 1:

"Seeing" is used as a euphemism for dating:

"Sam's not exactly a gay man. He's a transgender. So technically Mark'll still be seeing women."

And "seeing" can also be used for a relationship as in:

"You know that cute guy in the marketing department? We're seeing each other."

Solution 2:

Courting comes to mind, if you're looking for something that implies an intent to solidify a relationship at some point in the future as something exclusive.