Pretty much what the title says cause she gives off heavy tsundere vibes so it'd be cool if you could continue your previous "relationship". I'm only on day 26 in case I did things too early

You can bring Katarina to your side before and or after you bring Mario down but you can't invite her to your Studio if that's what you're wondering ( don't know about future updates though ).  

After Mario forced Katarina to spread her legs for you, go to Mario's Villa and straight to the Terrace. If you meet Emma, go to the Terrace again the next day or days after or the next week. When you're able to meet Katarina, simply repeat the dialogues over and over until she starts begging for more sex with you and completely fallen for you. ( This process only works when Katarina is at the Terrace, not Library. )

This process is also necessary if you want to unlock her scene at the Mall as well, which is, again, pure RNG.