'proceed with the call' is correct and usable in written English.
You can use it to refer to continuing a phone conversation. For example, "Please proceed with the call while I take notes."
One smoker could not be contacted and nine refused to proceed with the initial call.
Education reformers were eager for Anderson to proceed with the plan she calls One Newark, which includes turning three of the district's lowest-performing schools over to charter schools.
Mr. Jones said it made more sense now to proceed with the larger project, usually called the reformulation project.
The socialist government recently filed a shelf-registration with US regulators to proceed with the issue, in what officials called a prelude to the country re-entering capital markets.
But a quorum of the board — five members — voted unanimously during an April 13 conference call to proceed with the audit, according to the minutes of that meeting, a copy of which was distributed to all committee members and obtained by The New York Times.
The provider then sends you a quote or calls you, and if you proceed with the service, you book and pay directly with the professional.
Chicago papers called fo the House Judiciary Comm. to proceed with the impeachment investigation.
The officers called their supervisor, who told them to proceed with the arrest if Brooks didn't comply.
Then proceed with the recipe.
Reheat gently, and proceed with the recipe.
