In the following overview, we only look at frequently attainable positions where you use a system instead of rigid theory. All positions where you need to memorise a lot of sub-plays are discarded (e.g. Caro-Kann).
Attainable, flexible and systematic Openings
Catalan
d4 Nf6, c4 e6, g3
London System
Can be played regardless of what black does
Jobava-London
less common than London, faster, more open
d4, Nc3, Bf4
queenside knight develops to c3 instead of the usual d2