The question to ask yourself is the following: is it the Service Innovation Center that was expanded in size, or is it the number of partner companies within the Service Innovation Center that was expanded?
Based on what you have written, I think you are meaning to say that the number of partner companies within the Center increased. Therefore, an adequate correction would be the following: "The number of partner companies within the Service Innovation Center was expanded from four to ten."
This use of "expanded" technically works in my correction above; however, I think "increase" would be a better fit here, considering you're talking about a number. Numbers typically increase, not expand. Objects (like a room, a balloon, even a body of water when frozen) typically expand.
Alternatively, if you wanted to talk about the physical size of the center (e.g., the dimensions of the room in meters), then you could say "expand." It would look something like this: "The Service Innovation Center was expanded to include six more partner companies for a total of ten." The only problem with this is that "expanded" implies an increase in physical size. A native English speaker will read this as, "The dimensions of the Service Innovation Center expanded in size. With more room, the Center could now hold ten partner companies, rather than four." You see here that the emphasis is on "hold" in the literal sense as it relates to the size/dimensions of the Service Innovation Center.
What I think you really mean to say is that the number of partner companies a part of the Service Innovation Center increased in number. That is why I recommended my first edit.
I hope this helps!