File under Things You Thought Already Worked.
For awhile, I too thought multiple Marketo forms on the same page worked as long as they had different form IDs (though I always knew there was a problem with 2 or more of the same form).
But no, even different forms don't really work. The only multi-form scenario that works out-of-the-box is different forms that have zero visible fields in common. Since Email Address is found on almost all forms, it's almost certain that multiple forms won't be fully functional without the fix below.
The problems with multiple forms all relate to the HTML ID attribute.