How can I output second search form with another form ID?

Hi there,
I use Bootstrap and D7 and I need to output two search forms with different design (another placeholder, icon and text for button etc). For single search from I not have any problem, I use theming via form_alter custom function into template.php.
I think, for the problem solving I can output second search form with another ID, then change form via form_alter. But I not have any ideas, how can I render second search form with new form ID.
Anybody help my? Thx for any answer.
Regards, Anatolii.

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