Since each stroke is a specific size and changing the brush size to try to make the stroke bigger only makes the stroke "fatter", the only thing I can think of is to:
1. Playback the Stroke once on a Canvas just large enough to contain the Stroke.
2. In the Canvas menu, choose Resize and make the stroke as large as you want it.
3. Create a New Layer and choose an appropriate brush variant.
4. In the Brushes menu, choose Record Stroke and trace the enlarged stroke.
5. In the Brushes menu, choose Save Stroke.
6. Continue as usual on a large enough Canvas to accommodate the enlarged Strokes.
NOTE: Not sure if I missed something. It's been years since I played with that feature, but I found that the recorded stroke, when played back, was largely missing. The Stroke I painted was a looping stroke that I named "string" and only the first part of the looping was there when I used the Playback command.
If anyone has a suggestion, please let us know.
If this idea seems like it should be workable, play around with it Ken and maybe you'll figure out what I did wrong (if anything).
Another idea is to create a Script then play back the script after first opening a larger, higher Resolution Canvas.
If you've never done this, hopefully you'll find instructions in Painter 12 Help Topics and/or someone like David Gell will come along and share his magical script-making knowledge.
Happy New Year!