Pipefitters represented by the GMB union have voted in favour of action following a similar move by their Unite colleagues.
Balfour is working for main contractor Petrofac on the site located to the east of the established Sullom Voe oil terminal on Shetland.
The dispute centres on a claim for an additional £50 per day to compensate for the alleged failure to provide suitable accommodation for members and an additional claim for payment for lengthy traveling time undertaken each day.
Workers employed on the job are housed on a giant barge at Lerwick harbour.
The Sella Ness Accommodation Facility opened in July 2011 and can accommodate up to 850 people.
The accommodation facility includes a shop, library, laundry, internet cafe, restaurant, gymnasium and bar, as well as a medical facility and five-a-side, all weather football pitch.
Harry Donaldson, Secretary GMB Scotland, said: “GMB will seek urgent talks with the main contractor to convey to them the ballot results and impress on management to need to seriously address the long running issues involved in this dispute.
“The employers need to sit up and take notice of this overwhelming vote and put forward an offer to resolve this long running dispute.”
In a statement, Petrofac told The Scotsman: “Petrofac takes the welfare of its workers very seriously and is committed to working with all parties to reach a satisfactory outcome while delivering the project successfully.
“We are surprised at this decision – everyone who is provided with free shared living accommodation was made aware during recruitment and when offered the role that the accommodation provided was on a “shared” basis, and they signed a waiver agreeing to this at the beginning of their employment.
“This is part of a very attractive package that includes a competitive salary (higher than they would able to command for the equivalent work on the mainland). However we have always aimed to maintain a constructive relationship with the unions – and we’ll be looking to meet quickly with them to see how we can move forward on this issue.”