This form is not so rare as one might think.
What was she doing when you entered the room?
To be interviewed for a job: see passive below
She may have been being interviewed for a job. [when some x occurred or was occurring]
What were they saying when the news of the accident was announced?
To be questioned by [someone]: see passive below
They may have been being questioned by the police at that point.
The passives: being questioned, being interviewed, being told, being groomed (dogs), for example, easily lend themselves to: may have been + being been (action verb in passive). This is common in speech.
There are no "other ways" to express these ideas. It is used to express something that may have been being done at a particular time in the past.