In theory it is possible to obtain all levels of civillian security clearance of any person who is not a Green card holder nor a US Citizen.
It is very cheap for a company to obtain a security clearance for a person who is a US Citizen, but for high levels of security clearance for a person who does not have US Citizenship or Green Card, they have to run a background check, plus send investigators to the place you grew up and interview your school teachers and your neighbours and find out if you had any radical ideas while growing up. This can cost a lot of money. There are several instances where private companies and government will spend a lot of money to obtain security clearance for foreign nationals. One example is a Russian Cosmonot flying on a US Space mission.
Again that is a civillian security clearance....millitary security clearance is another story.