How to change an object's own Workplane (and thus its own CS):
For a 2D object, establish the desired WP; select the object; go to Format|Place on WorkPlane.
For a 3D object, establish the desired WP; create a new 3D object; 3D-Add it to the target object, being sure to click on the new object first. I recommend that the new object be a Sphere, very small compared to the target object, and that you place it at the target's Center of Extents before adding. In most cases, the sphere will be swallowed by the target object and for all intents and purposes will no longer exist. If the target's COE happens to be an empty spot, leaving the sphere exposed after adding, you can Explode the result one time -- which will separate the sphere and the target into separate objects -- and then delete the sphere.