This is possible with a pretty cool attachment from Amend2 Magazines.

The product is called the Amend2 S300 Hybrid Grip Module and it allows you to seamlessly attach a Sig P320 slide to a custom Sig 365 grip.

Compatible with Sig Sauer P320 style compact and full-size slides (subcompact compatible with use of compensator)
Compatible with Sig Sauer P365 style 10, 12, and 15-round mags.
Compatible with all Sig Sauer P320 style holsters.
Full-size accessory rail allows attachment of full-size lights and lasers.
Utilizing P320 style slides allows for use of full-size optics.
Covered by the Amend2 Lifetime Warranty.

Definitely go check out their website and be sure to let us know what you think of this product.