I thought that is what commas are for, to place the modifier on one side or the other.
Eats shoots and leaves...
Seems as though proper placement of the modifier could prevent ambiguity.
Is it a dangling participle surrounded by a diphthong.

Some folks just need modifyin'...
Studies show that reading can often improve memory.
And:
Studies show that reading often can improve memory.
The addition and use of “can” eliminates the squinting modifier.
A squinting modifier with dangling participle is obscene.
The same goes for the use/nonuse of hyphens, especially in headlines. There’s a big difference between “man eating lion” and “man-eating lion.”
John 21:20 Then Peter, turning about, seeth the disciple whom Jesus loved following; which also leaned on his breast at supper, and said, Lord, which is he that betrayeth thee?
Blame social media.
We should embrace braces.
“Studies show that {reading often} improves memory.”
“Studies show that reading {often improves} memory.”
You’re welcome!
Many years ago, we were taught to write the adverb last: “The house that got a new roof was sold recently.”