The real 'funny thing' is most of the recommended stuff here is hardly 'today'. The reason is simple. Most of today's music is a disaster, musically speaking. So, I've been reading this one interested myself.
I'll make my statement recommending two bands (out of many more available). For the sake of it we'll have to jump in the time machine and travel some 45 years back. One of them not always strictly melodic, but boy, were they proficient, daring, brilliant, creative, never commercial, pushing the boundaries of pop music! The other one is more melodic and mesmerisingly beautiful. And yes, in both cases there're more than 3 chords/melodies/harmonies/time signatures. AIMHO. Happy listening!