Turn yarn into tweed yarn?

How can I take a simple wool yarn and add flecks of other yarn to turn it into a “tweed” yarn?

(I mean actual little chunks lightly mixed in – or even resting on the edge – as shown in my images of my beloved Berocco Inca Tweed yarn. I am NOT talking about the deeply intermingled threads of other colors that brands sometimes call tweed [right or wrong]. )

I’m spending the year in Chile and finding tons of great, local, handspun wool yarn. But I’m addicted to “tweed” yarn and, since I can’t find any, I’m hoping to learn a simple way to mix in little flecks to make my own tweed.

I’ve tried researching, but I keep only finding (A.) how to fully spin yarn from wool (and I’ll already be starting with spun yarn) and (B.) info about deeply meshing colors into yarn (not the sort of rough tweed I’m interested in).

Thanks for the help!

I don’t know if there is truly a way to make yarn look like that that isn’t spun like that. Possibly carry a multi colored or hand painted yarn along with a solid color? It may take some experimenting.