The answer is yes, but only in a very certain way.

Let's imagine that this is your current query:

 select foo , sum(bar) as sumbar from qux group by foo

Now, we want to add two more columns—let's call them other1 and other2—but we don't want to add them to the GROUP BY, because we still want only one row per foo in the results.

The very certain and only way that this will be allowed is by ensuring that the two new columns are inside aggregate functions.

Here's one example of many possibilities:

 select foo , sum(bar) as sumbar , max(other1) as maxcol1 , avg(other2) as avgcol2 from qux group by foo

What is NOT ALLOWED is to put "naked" columns (not inside aggregate functions) into the SELECT clause but leave them out of the GROUP BY clause:

 select foo , sum(bar) as sumbar , other1 , other2 from qux group by foo

This is invalid syntax, and only MySQL will run it (although they do warn you, in GROUP BY and HAVING with Hidden Fields, that results can be unpredictable).