Go after and Search high heaven

Go after verb - Go after with the intent to catch.

Search high heaven and go after are semantically related in look topic. In some cases you can use "Search high heaven" instead a verb "Go after", when it comes to topics like chase.

Go after and search high heaven are semantically related in look topic. You can use "Go after" instead a verb phrase "Search high heaven", if it concerns topics such as chase.