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？watashi to nanika nomimasen ka?|
|Won't you eat something with me tomorrow?||明日 私 と 何か 食べません か？ashita watashi to nanika tabemasen ka?|
Note that after 何か, we don't use the object particle を.
The verb 会う you've learned earlier can be used both with に and with と.
These sentences mean practically the same, but there is a slight difference in nuance, as the first sentence focuses more on the direction aspect of the action, whereas the second sentence has more focus on the mutual of shared aspect of the action.