Yes, Mycenean Greece flourished at a time when the Minoan was still very much alive, with Minoan Crete and Cyclades(which although its culture predated the Minoan, was influenced by its neighbor Crete) impacting the culture of mainland Greece. Minoan settlements existed very close to early Mycenean ones and interactions between the two continued for centuries.

Minoan trade extended far from even its near neighbors of Karpathos and Kastri, and Minoan cultural influences reached far-off Rhodes (where a colony was found), Cyprus and Egypt.

Around 1500 BCE Minoan culture started to wind-down (thought to perhaps be due to the eruption of Thera), and by 1400 Crete was under the control of Mycenean Greece.