The Hegemony is a welfare state dedicated in giving all citizens: housing, education, basic necessities (water, food, etc), and help with either finding employment or a job assigned by the Hegemony.
The Hegemony is built on the principles: prosperity, security, and conformity (as in equality/everyone has a place in the Hegemony since the Hegemony provides one common culture).
However large corporations still exist within the Hegemony. Some of these corporations like Prometheus step into Mega-corporation territory owning their own regions (company towns, reservations) as well as their own police forces (private security due to the scale of these corporations).
Could a welfare state (a unitary global government) coexist with megacorporations without many ramifications? What sort of economic or political compromises would have to be made?
Hegemony is still a free market. While any one can apply for state housing anyone can also buy their own housing. This applies to any of the state benefits. Any one can buy private instead of state goods if they want.
Hegemony would be considered "Big Government" since it is a unitary state with smaller regions having limited autonomy and legal authority.
The laws on monopolies have been relaxed with only "harmful" (as in causing stagnation) monopolies broken up.