For keep ~ing, we usually use the verb 続ける which means to continue, to keep, etc.
e.g.
食べる+続ける=食べ続ける
勉強する+続ける=勉強し続ける
Depending on the context, other expression could be more appropriate than ~続ける.
~てばかりいる for example, which means doing something all the time.
食べてばかりいる
勉強してばかりいる