Towergate has opened a tender to sell 23% of the business to Madison Dearborn Partners.
If successful, MDP would become the second largest shareholder in the company, behind Highbridge.
The 23% relates to the portion held by 35-40 minority shareholders, who individually have shareholdings of between 0.1% and 2% to 3% of the business.
David Ross, CEO of Towergate, said having another major strategic investor, on the same scale as Highbridge, would enable the company greater freedom to pursue major acquisitions.
"We realised the likelihood would be that later on in the journey, when we bring an acquisition to the table we would have had 23% of our shareholding that wouldn't want to back the investment because they weren't really strategic investors," he said.
"We're heading to that period now. It's very clear to those that are sitting on equity that we're planning to grow this company through acquisitions and expansion. Those minority shareholders need to decide where they sit with that."
Ross added: "Highbridge has been sorely taxed with the scale of our ambitions, so the idea that we can bring in another investor the same size gives us more firepower. We've got the backing we need now to do anything we want."
It is understood that MDP - which has a stake in LA Fitness - has contacted 10% of minority shareholders so far and agreed a sale. The tender opened today at 3pm and will run for four to six weeks.
Ross said the offer to buy from MDP was a "fantastic endorsement".
"This is a gargantuan day for the business and for staff. If there was ever a moment we could stop talking about the past and start talking about the future, it's today."
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