"Running through them" x "Running them through": Diferença

For me it seems to be correct.

To run sth through - it seems to me it would change the meaning and would need a complement.

There is a difference of meaning.

(1) For the context you give, use "running through them" (going through them one by one).
Just as you can run through proposals, you can run through trees, run through your money (spend it all), etc.

"I think I’ve grasped the main proposals, but would you mind running through them once again?" (This makes perfect sense.)

"I think I’ve grasped the main proposals, but would you mind running them through once again?" (This does not make sense. See (2) below.)

(2) "Running them through" is used to mean "making them pass through an object or process".

"The appropriate way to handle this is by runing (SIC - running) them through the add-a-person tool using staff or faculty as is appropriate. ...(Google)."

You can run students through a battery of tests, army recruits through a series of physical exercises, etc. Also "He ran them through" can mean "He killed them with a sword." If you ever hear some tell a soldier "Run him through with your bayonet", run. Don't look back.

(3) And
"I think I’ve grasped the main proposals, but would you mind running them through once again?" =
"I think I’ve grasped the main proposals, but would you mind running them by me once again?"

"by me"?

Essa eu não entendi.

(a) "I think I’ve grasped the main proposals, but would you mind running through them once again?"

has the same basic meaning as

(b) "I think I’ve grasped the main proposals, but would you mind running them by me once again?"

Flávia, I had not copied (a) correctly.

Flavcia, "by me" = "through the agency of me" meaning someone else did it.

Flavia and Thomas, thank you both anyway. That did it!