You can do whatever you wish I suppose.
What type of ownership change are we talking about? Like transferring it to another person altogether? If so, I prolly would not recommend it. Are you looking to take someone off? Again, I would not recommend it either. In these situations, they would have to close and reopen, with penalty unless by court order.
If we are talking about adding a joint owner, or transferring the account into thier revocable trust, we would prepared a dated and revised sig card and certificate.
I don't repeat gossip, so listen closely...