You can but it’s up to each bank to decide… if you are talking about a car for example they likely will not because there isn’t enough value in it to cover the risk of you defaulting on your payment. If you are talking about an investment loan or a mortgage that has security for the amount you want then they will bend over backwards for your business.
I don’t see how you could because I would think the new bank would need to have the CD in their bank before they give you the secured loan. Obviously, you can’t put the CD in another bank because it is being used as security for the original loan. Talk to you bank where the loan and CD is about refinancing.
You could do it if your current financier agrees to get the loan restructured. Talk to them about this.