I don't know if a monmouth can be modified, but when I made a thrum cap, I started by knitting a monmouth cap, and every 3 to 4 stitches, worked a half hitched 6" to 8" chunk of yarn on the "working yarn" into the cap. I made the cap almost twice as large as I wanted it finished and then felted it by running it through the washing machine and drier on hot....
The biggest problem with a thrum cap is that it it way too hot to ever wear (even in Winter)... and people keep asking you about a "Bad hair day".....