The phrase "may have applied" is correct and usable in written English.
It can be used to express uncertainty about something that may have happened in the past. For example, "The qualifications for the job were complex, so I'm not sure if I may have applied for it."
Some surviving writings, however, indicate that contemporary writers may have applied the name to the harp.
The early humans may have applied the concoction to their skin for protection or simply decoration, experts suggested.
Thus, while 447,000 may have applied to work in the UK since May 2004, a great proportion of these will already have gone home.
One of his videos also suggests that he may have applied to join the Army at a recruiting station in Phoenix.
I'd like to think that if someone was hired over a serving deputy, who may have applied for the job, that they would approach it in a mature way.
However, the panel suggested Fabri may have applied for the licence to give her claim to the ownership of the painting – or that of whoever she was acting for – the air of legitimacy.
Many of those students may never have applied for federal financial aid and, therefore, were not offered federal loans.
Or at least that is how it appeared to the naked eye; television replays suggest Coates may possibly have applied the final touch.
In reality, the cap may not have applied to them at all if they were not locked in through one of the bank's early redemption charges.
The regulator is worried that firms may sometimes have applied their increased charges to too much of a customer's gas or electricity usage.
A further limitation is that this MMI was experimental hence the usual pressures, motivations and preparation undertaken by candidates in advance may not have applied in this circumstance.
