Is it possible to put multiple forms on a single page? This is for D6.

I am trying to make a coupon offer page. I wanted to have two forms for two different offers on each side of a page. Each form has a text field for the coupon code and its own submit button. The first form works okay; however the second form's hidden values seem to be overridden by the first form's.

I'm using hook_alter to alter the second form to make it different, but it still has the same form_id as the first. Is this what's causing my problems, or do I need to look/think somewhere else?

Edit: the two forms have the same form_id and form_token, but different form_build_ids.