Crown prince squash

Hi everybody, I am pleased to be among fellow veggie growers. I am growing the above for the first time. The plants all seem healthy and are steaming ahead with good growth and flower production. Should I restrict the number of fruits I allow to grow on each plant, in order to get the best quality fruits? Thanks .

As an F1 it might not put out too many.  I think they tend to be rather stingy so don't be too rash and go in before they've had chance to set fruit. Crown Prince are so good it would be a shame to miss any.   

Thanks to all three respondents. Very useful info.