Abano Healthcare's disaffected shareholders are calling for a special meeting to vote on removing Trevor Janes as chairman.
Peter Hutson, a former Abano director and who owns half its joint-venture audiology business, and his supporter, James Reeves, own about 19 percent of Abano and so have the right to call such a meeting.
Abano Healthcare says it will consider the request for the meeting and update shareholders in due course. However, Abano says its board remains unanimous in its support of Mr Janes and the company's strategic direction.
A number of the fund managers who hold major stakes in Abano say Mr Hutson doesn't have their support.
Mr Hutson has repeatedly said that Abano is poorly governed and accused Mr Janes of distorting the truth.
Last year, Mr Janes and the Abano board thwarted Mr Hutson's attempt to buy its half of the audiology business.
Earlier in April, Mr Hutson rejected Abano's offer to buy his half of the joint venture for $12.9 million, at least 37 percent higher than a valuation Mr Hutson commissioned.
But he dismissed the offer as a red herring which he alleged was designed to deflect from other issues, such as performance of the dental division and aspects of corporate governance.
Mr Hutson, who also owns half of Abano's joint-venture audiology business, was forced to resign from the board in 2013 after he supported a takeover attempt which, had it succeeded, would have resulted in him getting Abano's half of the joint venture for a nominal sum.