How can I change my stylesheet definition for a cell to optionally add a caption below?

For example, I would like to add a caption to my "Program" cells shown here:

like this (but with the option of right or left as well as centered alignment):

There are some caption-like things to be found in the docs:

But I would prefer to have the caption as part of the cell expression (not simply a separately styled cell put right below it)

I've tried CellFrameLabels, but I stumbled on a few things:

• Controlling alignments and styling
• Adding/removing them easily
• Auto-numbering

Related:

• Extending cell definition to CellFrameLabels definition