It is understood Assistant Chief Constable Bernard Higgins and Superintendent Kirk Kinnell are under investigation for the alleged offences at the Police Training and Recruitment Centre in Jackton, East Kilbride.
No wrongdoing has been admitted by any of the officers under investigation.
It comes as the force has appointed two new temporary assistant chief constables days after the suspension of Mr Higgins.
He was one of four officers suspended on Friday as part of an inquiry into criminal and misconduct allegations which saw a further two officers placed on restricted duties.
Deputy Chief Constable Iain Livingstone – the most senior active officer in the force while Chief Constable Phil Gormley is on special leave following misconduct allegations – announced the appointments.
Speaking at a Scottish Police Authority meeting, Mr Livingstone said the board had agreed to appoint chief superintendents Gillian MacDonald and Alan Speirs to the temporary ACC roles.
Mr Livingstone said: “This is clearly a challenging time for policing in Scotland and my focus continues to be on meeting the operational and organisational challenges we face, and providing the leadership of policing that the people of Scotland rightly expect.
“I remain in charge of day-to-day policing, strongly supported by my colleagues in the force executive, together with the command teams in every part of local policing in Scotland, as well as specialist national departments.”
Opposition parties at Holyrood have called on justice secretary Michael Matheson to “get a grip” on Police Scotland.
Scottish Labour’s justice spokeswoman, Claire Baker, said: “We have lost two chairs of the SPA, one chief executive and one chief constable with another under investigation.
“As a result, the public are losing confidence and the good work of dedicated rank and file officers undermined.”
Liam Kerr, the Scottish Conservative justice spokesman, said: “The justice secretary can’t duck questions forever; he must face parliament and explain exactly how he is going to fix the chaos that’s engulfed Police Scotland.
“With daily reports of mismanagement, misconduct and interference Michael Matheson must finally take responsibility and admit he doesn’t know what’s going on or how to fix it.”