You want to be able to search for things like
john AcMe Corp. in a crud's quick search box.

if quicksearch is set-up to cover fields first name, last name and company name, then it should return the correct customer.
So we need a word-based aggregation of AND conditions, so conceptually

WHERE
(LASTNAME LIKE %john% OR FIRSTNAME LIKE %john% OR COMPANYNAME LIKE %JOHN%) AND
(LASTNAME LIKE %AcMe% OR FIRSTNAME LIKE %AcMe% OR COMPANYNAME LIKE %AcMe%) AND ...

If it would be really nicely made, we could concatenate search string, so searching for:
john "AcMe Corp."

would search for
(LASTNAME LIKE %john% OR FIRSTNAME LIKE %john% OR COMPANYNAME LIKE %JOHN%) AND
(LASTNAME LIKE % AcMe Corp.% OR FIRSTNAME LIKE %AcMe Corp.% OR COMPANYNAME LIKE %AcMe Corp.%) AND ...

Not complex, but powerful.