Unite said Ineos had questions to answer over how emails appeared in newspapers last year during a dispute at the refinery.
The union said it had reported Ineos to the Information Commissioner and had started High Court action against the company.
Unite's Scottish secretary Pat Rafferty, its legal director Howard Beckett and former convenor Stevie Deans have all lodged requests under the Data Protection Act with Ineos, public relations firm Media Zoo and public affairs agency Portcullis.
Mark Lyon, a former Unite convenor at Grangemouth, who was sacked by Ineos after 25 years of service, has also demanded that the company release data and information held on him.
Mr Beckett said: "Ineos, Media Zoo and Portcullis all have questions to answer about their actions and how confidential emails found their way into national newspapers.
"If these companies want to avoid suggestions of a cover up and appearing to have a complete disregard for the law, then they need to come clean.
"No company is above the law and they should be in no doubt that we will pursue every legal option to force them to comply with the law and hand over the information that we, as individuals, are legally entitled to."
Ineos said in a statement: "We have not yet received any documentation but we are very confident that the company has done nothing wrong and will be fully vindicated in any court action.
"Since the ending of the dispute at Grangemouth, Unite has continued to try and undermine the plant.
"Ineos dropped its own legal actions against the union only to discover that Unite has chosen to issue new writs against the company.
"Unite also attempted to sabotage a new Ineos initiative to set up a works council at the site that embraces all workers (not just the trade unionists) by urging its members to boycott the process."