Multiple forms on single page? Is it possible to put multiple forms on a single page?

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?

The two forms have the same values for "form_id" and "form_token," but different values for "form_build_id."
If you want to add the same form multiple times, you need to implement hook_forms(). See node_forms() for an example.

This allows to use different form_id's, which all point to the same form builder function. For example, you can use yourmodule_some_form_$i and then use hook_forms() to point these to yourmodule_some_form.

See http://www.mohitsharma.net/content/how-show-same-form-multiple-time-page for an example