Offshoot rhymes with:
crapshoot, overshoot, parachute, absolute, arrowroot, attribute, bandicoot, bitterroot, breadfruit, constitute, convolute, countersuit, crapshoot, destitute, electrocute, execute, grapefruit, institute, jumpsuit, lawsuit, malamute, overshoot, pantsuit, parachute, persecute, prosecute, prostitute, reconstitute, resolute, restitute, spacesuit, substitute, sweatsuit, swimsuit, telecommute, wetsuit, wintermute
Offshoot sounds like:
obesity, obfuscate, object, objected, oboist, obsessed, obst, officiate, officiated, offset, opacity, opposed, opposite