Can you really be in love, but still have feelings for someone else?

I've been debating with a friend about this. I don't think you're truly in love with your partner if you have feelings for another person. I don't just mean finding that person attractive, or having a mini crush that only lasts a day. I'm talking about flirting with this person, feeling the need to hide the relationship from your partner etc. My friend thinks you can do all that and still be madly in love.