Employees were involved in the original RFP to outsource facilities maintenance, but no responses satisfied the request.
The council on Tuesday was faced with sending out a modified version of the RFP, and Muir claimed such an action requires another round of employee input.
She managed to convince Mayor Eric Bever, but not the council's three other reliable votes for city outsourcing.
In a 3-2 vote, with Bever and Councilwoman Wendy Leece dissenting, the council approved sending out the RFP.
"I was hoping to maybe avoid another $2-million lawsuit here," Bever said after the vote.
The city has racked up hundreds of thousands, if not more than $1 million, in legal fees in the last year defending itself in a lawsuit from city employees over proposed outsourcing.
Earlier in the meeting, the council unanimously passed a resolution opposing an Orange County Transportation Authority proposal that adds to toll roads to the San Diego (405) Freeway through Costa Mesa.
Criticized as the most expensive of three freeway widening options to address traffic, OCTA's Alternative 3 creates two toll lanes in lieu of a regular carpool lane and costs $1.7 billion while still falling $680 million short in funding.
It also requires years of construction in Costa Mesa and the rebuilding of the Fairview Road bridge, which was reconstructed just three years ago with $7 million of city money.
Nevada Avenue resident Janice Baker complained that Alternative 3 moves the freeway sound walls closer to her home.
"It becomes a block wall prison," Baker said, saying she spoke for many of her neighbors who live near Moon Park and the Santa Ana River. "We are totally, totally opposed to option three."