Alternative to standart countifs function needed

Here is a story... columns A,B,C,D,E is a list,(can be formated as a table) and contain variables in form of numbers.These numbers are from 0 to 37. Need to count how many times each individual number in column E corresponds to the given sett of criteria (columns A,B,C,D). Problem is that l need to account not for individual sets of these criteria, but for groops of them. Groops are to be specified in other worksheet. I can not use ">" , "<" as a criteria argument due to the nature of variables.
If COUNTIFS function would accept any one of values in specified range of sells as valid criteria, it would look like this
=countifs('Sheet1'!A:A,A1:A18,'Sheet1'!B:B,B1:B18...)
Any ideas what could be used?