Hello,
I have an existing belowground sewage-ejector system that was added when I remodeled my basement 3 years ago and added a full bathroom. I would like to know is can you add a utility sink that will empty into the sewage ejector system?

Yes

Chuck

Will the new laundry sink be within 5 feet of the lavatory? If so, you can tie the drain of the laundry sink back into the lavatory drains where it will be wet vented. Otherwise you could tie back to the lavatory drains and vent the laundry sink with a AAV if code allows
Does this work for you? Let me know, Tom