In a sign of worsening of relations with plant owner Ineos, Unite will debate whether to link backing for Labour at Westminster and Holyrood with support for nationalising the company's operations without compensation.
Tory MSP Murdo Fraser said it was clear the union had a "stranglehold" on the party.
Unite's shambolic attempt at influencing Labour's Westminster selection contest in Falkirk, in which the union signed up over 100 new members in a bid to help their favoured candidate, had huge political ramifications.
The sign-up, which was linked to the Ineos plant at Grangemouth, was criticised by Labour leader Ed Miliband and led to the party rethinking its links with all its trades union affiliates. It also spiralled into a major industrial dispute.
Ineos accused Stevie Deans, at that point the plant's shop steward and Unite Scotland's chair, of using company time and resources to work on Labour Party business.
That row led to Unite backing strike action and was followed by Ineos threatening to close Grangemouth. The employer also insisted on swingeing changes to workers' terms and conditions. High-level political interventions led to a last-minute agreement between Ineos owner Jim Ratcliffe and Unite, but the dispute left the union feeling wounded and Deans out of a job.
It also cost the Scottish economy an estimated £65 million.
The Sunday Herald can reveal Unite will reopen the Ineos issue at its UK policy conference in June. A copy of the preliminary agenda contains a motion signed by two Scottish branches.
It condemns the "threat by Ineos's Ratcliffe to shut down operations in Grangemouth" and noted that it was "unacceptable" for "one individual to be able to wield such power".
The motion also commits Unite to "campaign for the nationalisation without compensation and under workers' control of all Ineos assets in the UK".
It called for this demand to be a "major focus" of the union's campaigning in the run-up to the next Westminster and Holyrood elections, including "withholding support from any candidate who does not support that demand".
Unite is the biggest union donor to Labour, but the party has not come close to backing calls to seize any of Ineos's assets.
A Labour source said: "You can understand why Unite have concerns about the ownership of Ineos, but they clearly have not learned any lessons from Falkirk if they think the solution is to hold a gun to the head of Labour candidates. It is crazy."
If passed, the motion could result in only a handful of left-wing Labour candidates receiving funds from Unite and starve Miliband of resources. It would also hamper Scottish Labour leader Johann Lamont's bid to become the next First Minister in 2016.
The row between Ineos and Unite was one of the most bitter industrial disputes in years. The company was accused of treating the plant's workers in a brutal fashion, while the union was believed to have over-played its hand by backing strike action.
Another motion to the conference, from branches in the northwest of England, calls for Unite to cut the money it gives to Labour.
Murdo Fraser said: "It seems that no matter what Ed Miliband and the Labour Party say, the unions still have a stranglehold on the party.
"With their massive funding of the party they are always going to have a significant influence, including the selection of candidates.
"Despite the Grangemouth dispute costing the Scottish economy £65m, the unions do not appear to have learned any lessons."
A Unite spokeswoman said: "It is in the preliminary agenda. It will have to go through due process before being debated and could well change."
She added: "It will be for conference to decide."
An SNP spokesperson said: "It is of course a matter for trades unions which candidates they wish to support and for what reasons, but this resolution obliges Johann Lamont to set out exactly what Labour policy is."
An Ineos spokesman declined to comment, as did a Scottish Labour spokesman.