'may encompass' is a correct and usable phrase in written English.
It is typically used to indicate that something can include or cover a wide range of related things or ideas. For example, you could say "The discussion may encompass everything from current trends in fashion to the latest technology."
"Islamist," it says, may "encompass a wide range of Muslims," from mainstream politicians to jihadis.
Jurisdiction is conferred by the minister of justice and may encompass any written law, but punishment powers are limited.
It has networks in 500 markets, not in 500 cities. (A market may encompass more than one city).
Trafficking networks may encompass anything from a few loosely associated freelance criminals to large organized criminal groups acting in concert.
In permanent modular construction, a module may encompass parts of more than one dormitory room or may be as small as a single bathroom.
The academy acknowledged that case management must be highly individualized: "Each concussion is unique and may encompass a different constellation and severity of symptoms".
On the cusp of womanhood and all it may encompass – fertility, sexuality, pregnancy, motherhood and menopause – there is a natural course anticipated beyond the physical changes: love, relationships, children.
Even accounting for people who have more than one condition, statistics suggest that the city's long list of red flags may encompass as many as one in three people.
Applications designed to execute on human computation systems may encompass one or multiple tasks.
It has been shown that this condition may encompass a large class of nonlinearities.
Self-employment is a form of labour market status which may encompass a wide range of different activities.
