What does the Japanese word mata aimashou mean?

'Chaimashou' grammatically is volitional/suggestive form of '-chau' which is an auxiliary verb (mostly used in informal context) added to the end of other verbs, adding a sense of "doing something to the end, completion or emphasis". However I have never heard of it being used in volitional/suggestive form. It would mean roughly 'let's.....' where in the blanks goes the meaning of the verb that precedes it.