Suyo, tuyo are used instead of the object. So in my opinion the answer to your question is no, you can not say ''la organización suya'' If you say ''your organization = su organización.
Suyo/a tuyo/a takes the name of an object. Mi madre y la suya/tuya. Mi coche y el suyo/tuyo.
As I am English, wait and see what the native speakers say.