Data compression with Turing Machine
Suppose the first byte of the compressed file indicates which decompression algorithm to use, and then you use that algorithm to decompress the rest.  Sure, you could do that.  Absolutely.  Some compression formats already do exactly this.

That said, it's also possible to view this as a single decompression algorithm.  The master algorithm looks at the first byte of the file and then branches to a subroutine that handles the rest of the file.  That can be considered a single algorithm.  So at a fundamental level there is no fundamental distinction that can be drawn.