Optional Property Extensions With State

[Peter]

I'm currently using type composition in my design to extend an existing type, but I'm curious if F# optional extensions might also be useful.  I understand how to implement optional extension methods, but I'm having trouble with optional extension properties.  It appears that optional property extensions are possible (https://msdn.microsoft.com/en-us/library/dd233211.aspx), but it doesn't appear that they can include their own state/backing store.  The few examples I've seen only use the existing state available in the type being extended and act more like member functions than properties with a backing store.  Does the F# compiler allow for a manual/automatic backing store with optional property extensions?  If so, please provide a small code sample.

Thank you,

Peter Santoro