WASHINGTON (CNN) -- The Senate may face dueling resolutions next week when senators who objected to language in a proposed resolution on President Bush's plan to increase troop numbers in Iraq present their own proposal.

An aide to Sen. Susan Collins, R-Maine, told CNN Friday that Collins, Sens. John Warner, R-Virginia, and Ben Nelson, D-Nebraska, and others worked late into the night Thursday and agreed to language for the new resolution. The aide said, however, that the senators would not discuss the content until Monday, when they have scheduled a news conference.

Collins is one of several Republicans who oppose Bush's plan to send more than 21,000 additional troops to Iraq, but she and others objected to language in a resolution proposed by Sens. Joe Biden, D-Delaware, Carl Levin, D-Michigan, and Chuck Hagel, R-Nebraska.

In particular, Collins noted that the Biden-Levin-Hagel resolution discussed issues other than Iraq, such as North Korea, and used the word "escalating" to refer to the troop increase, a term she and other GOP senators considered partisan.

Warner, the influential ranking Republican on the Senate's Armed Services Committee, has so far avoided saying whether he agrees or disagrees with the president's plan, but is said to have been working behind the scenes for some time to build support for a compromise.