"may possibly be" is correct and can be used in written English.
You can use it to show that something is uncertain or possible. For example: "We may possibly be able to find a solution to this problem."
These may possibly be seen by people you do not know, or possible employers.
Juárez may, possibly, be turning a corner.
Starscossed may possibly be one of my favourite books.
These people may possibly be under Agents to some principal at Bristol".
It may possibly be one of the great international accords of the post-war era.
Encourage bilateral agreements Copenhagen-style agreements may possibly be fruitful, but could flounder.
In this fashion, whatever vengeful local gods were ired by millennial hubris may, possibly, be gratified.
The glowing coda of "Ravelstein" may possibly be thought of as otherworldly.
The tiny proportion who are well and truly deaf, may possibly be better off.
This finding may possibly be ascribed to the water gas shift reaction.
The 5h may possibly be used as lead compound for developing new anticancer agents.
