Take this sentence as an example:
You may want to consider placing the money in a more conservative portfolio and move on with life.
The expression "move on with life" is fine by itself, but "moving on with life" brings in ample amount of Google results as well. But shouldn't "move" be in gerund form much like "placing"? So:
You may want to consider placing the money in a more conservative portfolio and moving on with life.
When in doubt, I like to shorten the sentence to get rid of the noise, to something that is still structurally the same. Such as
You may want to consider burning the money and moving on with life.
Here the two verbs are much closer and I wouldn't even consider writing move.