Assuming that some collection fields are the same, can you search multiple collections in one search/search form?
Yes. Treat the collection parameter as the channel parameter. Multiple collections are searchable, even if the collection fields are different.
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Read more about the concept of Low Search in the Primer: gotolow.com/blog/a-low-search-primer and this EESE answer: expressionengine.stackexchange.com/a/1157/172 – Low Jan 9 '13 at 13:59