The negative form is often used together with the question particle か to invite someone to do something in a polite way.
The particle と can be used to mean with. In later lessons you will learn more uses for the particle と.
|Won't you drink something with me?||私 と 何か 飲みません か？watasi to nanika nomimasen ka?|
|Won't you eat something with me tomorrow?||明日 私 と 何か 食べません か？asita watasi to nanika tabemasen ka?|
Note that after 何か, we don't use the object particle を.