Disclaimer: I'm not all that familiar with WWW::Mechanize, so I may be missing something, but...

Are all four submit buttons part of the same form? If not, then you can probably just use $agent->form(3) to select the form that contains the appropriate button and then click() it.

If you have three buttons with the same name in the same form, then I don't think there's support for that in WWW::Mechanize (again, unless I'm missing something). It might be worth creating a patch or request and submitting it to the modules maintainer.

bbfu
Black flowers blossum
Fearless on my breath