There is a larger hoop available for your machine (SA434K) but it will not allow you to embroidery a design larger than a 4x4. What it does is allow you to embroider on a larger area without rehooping your garment. It is a multi-position hoop that allows you to do move the hoop on the machine (it has multiple positions that it can attach to the machine.)
A temporary fix until you outgrow your machine 
.