Staff at fashion group Ted Baker allege there is a culture of "forced hugging" by the firm's founder and boss, which they are now demanding be ended.
A petition, launched by an employee, also accuses 62-year-old Ray Kelvin of inappropriate comments and behaviour.
"It is part of a culture that leaves harassment unchallenged," they claim.
The company, which issues a trading update on Thursday, says hugs are "part of Ted Baker's culture, but are absolutely not insisted upon".
It said Mr Kelvin greeted many people with a hug, "be it a shareholder, investor, supplier, partner, customer or colleague".
The petition on the workplace website Organise had more than 2,000 signatures by Sunday evening.
It is also claimed that as well as engaging them in unwelcome embraces, the brand's founder asked young female members of staff to sit on his knee, cuddle him, or let him massage their ears.
They also allege that millionaire Mr Kelvin, who launched Ted Baker more than 30 years ago, regularly uses sexual innuendo.
'Clear and robust HR policies'
But Ted Baker also said that the matters raised in the petition were "at odds with the values of our business and those of our CEO".
And it said it would "ensure a thorough independent investigation is carried out" into the allegations.
Another complaint made in the petition is that previous complaints have been ignored.
"Please set up a way of reporting harassment to an independent, external body - HR has done nothing with the reports of harassment to date," says the petition.
But the firm said there were "very clear and robust HR policies in place to provide all employees with a wide range of reporting options for any issues that they might encounter, including a completely confidential and anonymous, 24/7 helpline".
Ted Baker, named after a fictitious alter ego of Mr Kelvin, opened its first store in Glasgow in 1988 and now has 544 outlets worldwide selling fashion and accessories.
Mr Kelvin is worth £522m according to the Sunday Times Rich List.