It will have to be a multi-pass process.
(1)  Sort by your least important columns first.
(3)  Now sort by your more important columns.

I can actually count, and omitted step 2 deliberately.  I do not know whether Excel's sort algorithm is "conservative" or not:  ie whether when all three keys are identical it preserves the initial order.  Non-conservative algorithms tend to be more efficient, so I would guess that Excel's is non-consrevative.  (Not that I usually place the words "Microsoft" and "efficient" in the same sentence.)

If Excel's algorithm is conservative, then steps 1 and 3 are all that is required.

However if it is not conservative, you will have to create an additional temporary column in your data.  After step 1, fill this column with the sequential numbers 1 through N, from top to bottom.  This must be the actual number, not a formula.  (You can use a formula for initial generation of the integers, then "copy/value" the results over the top of themselves.)  Now you are ready for your second invocation of the Excel sort operation (step 2 above):  the only catch here is that this new column must be included as the least important sort key.

So, two sort operations gets you sorted on five columns.  Steps 2 and 3 can be repeated as many times as necessary to accommodate as many columns as you need.

This can be reduced to a single operation by recording and/or writing a macro to do the hard yakka.

HTH