Cooperation, how to use it in a question?

Is it correct to say:

Would you like to start a cooperation (with us)?

Or should it be: Would you like to cooperate (with us)?

I feel like the first sentence is wrong, as it sounds to much like saying would you like to start a corporation (with us)? (with a dutch accent) but the second sentence suggests more aggressive style of asking for someone to cooperate with you. Maybe there is a better way to ask this question?

edit

I should also state I am referring to a international business venture / collaboration. Where for example we would like to sell electronics on our website from his/her company for a small commission or put your vacation house up for rent on our website for a small commission. You would eventually sign a contact to do this(of course).

So what I'm asking is: is it correct to ask the above stated questions? or is there a better way?

Note: It should not sound like you would want to 'hook up' with the person your talking to e.g. partnering relationship

Answer

Is it correct to say:

Would you like to start a cooperation (with us)?

Because the noun cooperation has a sense “The act of cooperating or being cooperative” (wik.), one can re-form the above line as “Would you like to start an act of cooperating or being cooperative with us?” Such a question is grammatical and is semantically sound; that is, is not “incorrect”. However, both forms are clumsy and unnatural.

One might instead say “Would you like to start a cooperative venture?” or (more naturally) “Would you like to enter into a cooperative venture?” or “Would you like to enter into a joint venture?”.

Note, Google ngrams for partnering relationship,cooperative venture shows that partnering relationship is a parvenu, not on the charts before 1980, and only about 2% as common much of the time since then. However, partnering relationship seems to be on the rise, and cooperative venture on the decline.

Google ngrams for partnering relationship,cooperative venture,joint venture shows joint venture occurring typically about 30 times more frequently than cooperative venture and hundreds of times more frequently than partnering relationship.

From en.wiktionary, joint venture means “A cooperative partnership between two individuals or businesses in which profits and risks are shared”. A wikipedia joint venture article mentions related terms and points out some distinctions among different kinds of partnerships.