Sounds like you simply want the MAX() of the MAX(); in other words, use a subquery to SELECT the MAX() values for each of the columns, and then, in the outer query, SELECT the MAX() of the values of that subquery.
EDIT: Woops, maybe it's not that easy...
EDIT2: I'll be humble enough to let my brief moment of ignorance remain visible, because it definitely wasn't that easy (it never is, is it?).
Instead, what I came up with was to UNION the individual max values from each column inside the inner query I talked about above so that you get a column vector of max values (which is what MAX() operates on), rather than a row vector.
In other words, something like this:
SELECT MAX(max_column) absolute_max
FROM
(
SELECT MAX(value1) max_column FROM my_table
UNION
SELECT MAX(value2) FROM my_table
UNION
SELECT MAX(value3) FROM my_table
# etc. for all columns in the comparison
) max_column_values
;