Yes. You create the rules in this situation. You don't really need to provide explanation beyond what your rates are. So if your rent is $400 for 1 person to rent a room, then $400, $500, $600, $700, and $800 per month are all reasonable amounts for 2 persons to rent the room. - You set the rate based on: How quickly you want to rent the room, How much you want to rent to 2 people. - Wear and Tear, Utilities, Etc. are all reasonable explanations if someone feels they need more explanation.
As another user suggested you might not want to 'exclude' additional occupants, especially in advertising. - In most locations you can be as choosy as you want for someone renting a room in your own residence. (BUT advertising still can't be discriminatory.) Personally, I would probably charge a 'per person rate.'*** - This would likely eliminate any more than 1 occupant without directly stating it. (Why choose your place for '$800' if they can find somewhere else for '$500-$600?')
Best Advice you'll ever get: Don't ever rent to someone that can't put down first month's rent and deposit (As applicable for renting a room. We never charged a deposit for renting a room in our own house. Never really had an issue, but did regret not having a deposit when roommate moved out the last day of the month with no )
Better Best Advice you'll ever get: Don't rent to anyone with pets. - No exceptions.
***Note: This isn't exactly what I am suggesting above, but I do have a relevant example: I knew 2 single guys that lived with a Married Couple they were friends with. (Everyone same age) In their case, the per person rate was fair because they were sharing a 3 Bed 2.5 Bath house. The Master bedroom (Married Couple) was roughly double the size of the other bedrooms and had it's own bathroom. The smaller 2 bedrooms shared the other full bath. - So cost basically everything was fairly split right 'down the middle.' (Or split in fourths if you'd rather look at it that way.)