Modifiers describe other words or add detail. They need to go next to the words they’re modifying or confusion arises.

Example: “she served sandwiches to the guests on paper plates.” What? Her guests were on paper plates? Better to say “she served sandwiches on paper plates to the guests.”

Likewise “he met his old girlfriend on the way to meeting his new one” could imply that his old girlfriend was on her way to meet his new girlfriend. Better to say “on the way to meeting his new girlfriend, he met his old one”.