Sort grouped data while preserving structure / hierarchy

This seems to be a common problem, but I haven't found a solution, perhaps because I don't know what this type of sorting is officially called.

This example should make it clear. I want to sort the following data, primary ascending on left column, secondary ascending on right, while maintaining the grouped structure....

C	5
	7
	1
A	3
	8
	6
B	4
	2
	9

.... so that the result is this...

A	3
	6
	8
B	2
	4
	9
C	1
	5
	7

.... NOT this:

A	3
B	4
C	5
	1
	2
	6
	7
	8
	9

My foremost concern is botching the data -- Once saved, the wrong sort per above is irreversible. Further, in my case there are thousands of rows, and nothing contextually associating the columns, so I won't be able to fix corrupted data even if trudging through it manually.

Therefore, I don't want a method that fills cells or otherwise affects the original data, but rather puts the sorted data off to the side. A direct solution is of course preferred, but I'm open to helper columns, vba, multiple steps, etc.

Any help appreciated!

The results are OK, but the macro altered the original data which now shows 4 A values and 2 C values instead of 3 values each.

Is there a way to do it without filling or altering the original data, given the risk of corrupting it?

The original data is critical and must not be altered. Per original post: "I don't want a method that fills cells or otherwise affects the original data."
Yes, the original data can be duplicated to safely work on, but ideally I'd like to avoid that.