Occurrences of “to may be” in the form that the OP describes are rare in a Google Books search of books published between 1600 and 2009, but I did find two matches, from books published in 2006 and 2009. From Roopchan Lutchman, Sustainable Asset Management: Linking Assets, People, and Processes for Results (DEStech Publications, 2006):
We have heard the old sayings “What gets measured gets done” and “Without data you are just another opinion” many times and they may seem to may be simplistic but has real meaning in the business environment. The best of strategic plans and intentions can amount to very little unless there are clear goals, objectives and associated targets to ensure that strategies for success are being achieved.
From T. Hayashi and A. Myakoshi, “Land expansion with reclamation and groundwater exploitation in a coastal urban area: A case study from the Tokyo Lowland, Japan,” in From Headwaters to the Ocean: Hydrological Changes and Watershed Management (CRC Press, 2009):
Confined groundwater in the reclaimed areas shows different chemical properties with the inland part of the lowland. Chloride ion, hardness and potassium permanganate consumption value of groundwater in the reclaimed area are higher than those in the inland part. Considering the hydrological setting and the distribution of these components, there is no good reason to think that these components had been recharged to groundwater from the ground surface of the reclaimed area. Groundwater in the reclaimed area is considered to may be originally in the stagnant condition. The result of this study suggests that it is possible to use groundwater beneath the coastal seafloor as water resources, but more careful and sufficient evaluation of groundwater environment is required because groundwater in this area may be in stagnant condition.
Neither of these instances of “to may be” seems unintentional and neither involves a simple error of splitting “maybe” into two words; but the meaning in both instances would have been clearer if the authors had used the wording “to maybe be” or had reworked the relevant sentence to express the authors’ uncertainty more elegantly.
On the other hand, the phrase “to maybe be” is itself a fairly recent arrival in published writing. Easily the earliest match in a Google Books search is this instance from Anne Warner, Susan Clegg and a Man in the House (1907):
”Not me,” said Miss Clegg; “I ain’t got any give-up in me. I’ll keep on until I find it if I have to board Elijah Doxey till he dies or till I drop dead in my huntin’ tracks. But I see that my feelin’ towards him is n’t goin’ to be what it might have been if he’d been frank an’ open with me as I am with him an’ every one else. He seems frank an’ open, too—in other ways than that box. He read his editorial aloud night afore last an’ I must say it showed a real good disposition for he even wished the president well although he said as he knowed he was sometimes goin' to be obliged to maybe be a little bit hard on him. …”
The next matches for “to maybe be,” stretching from 1949 through much of the 1990s, occur in transcriptions of recorded testimony or in fictional dialogue. In fact, the earliest occurrence that a Google Books search found of “to maybe be” in a scholarly setting was from Colette Grinevald, “Living in Three Languages,” in Essays on Language Function and Language Type (1997):
One of my first courses in linguistics that Fall was phonetics, with Steven Anderson. I was grateful to be introduced to phonetic transcription early on, as I did not understand too much of the lectures. I took notes in French and started writing down phonetically those words that seem to recur often enough to maybe be of some importance, linguistically or perhaps just in general. I read those phonetic transcriptions to my household at dinner time.
On this evidence, it appears that “to may be” remains a very rare alternative formulation for the phrase “to maybe be,” which itself is far more common in informal speech than in formal (and copyedited) writing. For the time being, “to may be” is likely to sound like a mistake to most English speakers; but years from now, authorities may be pointing out that the wording has been attested in serious writing “since at least 2006.”
Related Historical Note
In the course of my Google Books searches, I was surprised to find a specimen of “to may be” in a treatise evidently written during the reign of Henry VI. From John Fortescue (who died circa 1480), The Difference Between an Absolute and Limited Monarchy ; As It More Particularly Regards the English Constitution:
And if it happyn that any Patent be made of any parte thereof [that is, of the King’s ordinary charges] to other use, that than the Patent to be voyde, and of non effecte : Which thyng, yf it be fermely establyschid, the Kyngs Ordinary chargys may alway be paid in hand, and the Provysyon of them may be alway be made in season ; which schal be worth to the Kyng the fourth or fifth part of the quantite of his expenss for his Ordynarye charges. This may in nothyng restrayne the Kyngs Power. For it is no Power to may alien, and put awaye : But it is Power to may have, and kepe to hymself. So it is no Power to may syne, and to do yll, or to may be syke or wex old, or that a Man may hurt hymself. For all thees Powers comyne of Impotencye.
In the 1714 edition of this work, edited by a descendent of the author, John Fortescue Aland, the editor provides the following footnote in connection with “to may alien”:
To may alien, to may have, i. e. to be able to alien, and to be able to retain, from the Saxon Verb, magan, posse, to be able ; which see before, in the word may.
In the earlier note, the editor observes that
mæg is the present Tense of the Saxon Verb magan, which signifies to be able, or to may, do a thing, as old Authors express it.
In this older understanding of "to may be," it seems, the sense was not "to maybe be" but "to be able to be."