If it looks like it has become a sort of thicket of separate stems this may be possible. What is it botanically? Usually mock orange is Philadelphus but since you are in the south perhaps something else, such as Choisya. The first you would only want to lift and divide when it is leafless, here these are just about to bloom.

Hi - Well mine is still in bloom and yes it looks like a thicket now. Here's a pic. from last year. Thank you. tina_2

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You can't divide Philadelphus like a perennial; most woody shrubs cannot be divided, in fact. You can cut rooted suckers or ground layer, but you can't dig up and split.

Dan

Depends on if it has grown into a clump of multiple stems springing from beneath the ground, somewhat in the manner of a lilac - something I have seen these do.

But if you merely want to make more, hardwood stem cuttings are often easy with this shrub.