I, together with Kati, am going for the movie tonight.
This sort of sentence is rarely uttered by native speakers. It's favoured by compilers of language exercises who want to see if poor learners (including native speakers) are aware of the lesser known 'rules' of English.
What we'd say in real life is:
Kati and I are going to the cinema (BrE) tonight.
I am going to the cinema with Kati tonight.
Kati is coming/going with me to the cinema tonight.
I am going to the cinema tonight. Kati is going/coming with me.