Resetting a sapphire

[FutureMidwife]

Hi all....
Long story short....I had a sapphire solitaire, I had it removed from its setting and reset into something fancier. Now I want the simple setting back. But with a twist. I'd like to have it set into a new basket...something with a hidden diamond or something else cool. So my question is this: can you remove a basket from a band and pop in a new one and set the stone in it? Am I making any sense?

Thanks in advance for any help!

 

[chrono]

Not sure about your question but I think whether you can/cannot do it will depend on the current design (peg head versus integrated head). Can you post pictures of what you have and what you want done?