Pratchett described "seeing odors" as the way werewolfs experience the world
Haru is right. Synesthesia is it's own conversation but it's not a real kind of 'sense.' I think the best way to do this is to split the possibilities into three types of real senses and pick the flavor that suited the plot. (Just to make sure it's more of a rational idea your player can work with instead of a word game.)
One where you sense more of what you already could, like an extra color representing ultraviolet light or infrared. It would probably be uncomfortable and confusing because it takes us years of our best brain development time to discern objects in our basic senses.
Expanded vision spectrum.
Detailed smells and tastes.
Long range or ultra fine hearing.
The cartoony ones like footprints highlighting for you would be a better understanding of what you could already see. That would have to be the Demon actively working to show it to you. They could even describe their assessments of a person like Sherlock Holmes, claiming to know their life story or whether they're lying.
Detective Vision from the Batman Arkham Asylum game.
Sherlock Holmes observations and deductions whispered in your ear.
Organizing many voices talking over each other (like a bar) into clarity (like a chat room.)
The last would be the more ESP, like a halfway between the previous two. Detecting when someone is near death with a black shroud around them (I think that's from Stephen King.) Or getting thoughts broadcast at you from other people by electromagnetic waves. You know how part of a song gets stuck in your head? Imagine an entire busload of people with that and you can hear it!
Emotion Sense from people you touch
Strong Thoughts heard as if over a bad radio
Shining (Like you're a battery powering and seeing events and shades of what happened before.)
Ugh, I wrote an essay. Sorry!