A previous poster mentioned "hybrid style" playing ( i.e. using a plectrum in conjunction with fingers).
So many players use that style these days that the lines between "flatpick" and fingerstyle are somewhat blurred.
I even saw some early Beatles footage where George was employing a hybrid technique.
Richard Thompson does a lot of hybrid picking, as does the wonderful Lucy Kaplansky ( I LOVE LUCY!). Indeed, Lucy, I think, plays exclusively hybrid style,
Hybrid has become my first choice style, and I would like to think that, if practised diligently, hybrid could cover everything that a pure fingerstyle and pure flatpicker could achieve.
I'm not quite at that point yet. But I am getting closer!