Janet,
Following your message, I tried a few googles in an attempt to find out if the word "Teamowners" would bring up anything. ...Two items on a list that came up do mention it. On the list is a post made on Roots Web - Anglesey, and another on Roots Web - Merseyside.

The google I used was: Horses - Team Owners, Liverpool, 1911.

You are right, it is to do with teams of horses, and the word Teamster shows up there as well.

My grandfather might have been grabbing employment as a cashier at any job he saw available. But on the other hand, he could have been placed (by his brother) with a company near the docks for a reason, maybe to do with goods coming off ships, and that would be where the Teamsters come into it.

Thanks for your help. I've heard the word Teamsters used in American gangster pictures but never quite knew what it meant.
Brian