No. There's no mechanism for saving sorts within Numbers - they are a kind of one-and-done thing.
There is a kind of workaround, which is that you can use AppleScript to initiate the sort. It's a little non-intuitive, but you could write separate AppleScripts for the different sort mechanisms you want and then invoke the script as needed.
Here's an example AppleScript that sorts by two columns:
tell application "Numbers"
tell document 1
tell sheet 1
tell table 1
sort by column "F" direction descending
sort by column "A"
end tell
end tell
end tell
end tell
Paste that into a new Script Editor document and click Run.
Hopefully the syntax is clear enough for you to be able to edit/amend to your own sorting needs.