Unfortunatley no but you be super efective on all types except three with one moveset
fighting type move: ice, rock, normal, dark, steel
rock type move: flying, fire, bug, ice
ground type move: electric, steel, rock, posion
ghost/dark type move: ghost, psychic
or ice type move: grass, dragon, flying
you must choose between the last two whichever you
choose will leave you with three types uncovered becuase of water.