Hospital bosses are meeting later to decide whether to transfer non-medical staff over to a new company.
Plans would see about 350 Yeovil Hospital support staff, including cleaners and porters, moved over to a subsidiary firm called Simply Serve, which the hospital would own.
Unison, the union, said the plans could have a "detrimental" effect on care.
The hospital said the move would protect jobs and ensure the continued quality provision of hospital services.
Under the proposals existing staff would remain on the same terms and conditions, but new employees would not.
Future staff conditions are yet to be confirmed.
'Refused to consult'
Helen Eccles, of Unison, said the hospital had refused to consult with unions on the plans.
A petition urging the hospital to defer the decision has been signed by more than 900 people.
She said: "It breaks up the NHS team and puts staff outside the nationally-agreed terms and conditions and we believe it could have a detrimental effect on patient care."
The hospital said a month-long staff consultation received "just two pieces of staff feedback".
A spokesman said: "We are aware that Unison is opposed to this plan and have continued to work with their representatives since August to describe how this new company - which is 100% owned by Yeovil Hospital - will protect existing jobs, create new employment opportunities in the local community and ensure the continued quality provision of these crucial hospital services."