"That is an expensive, black handbag," would suggest that the emphasis is on "expensive" as opposed to on "black." (i.e. That is a black handbag, which is also expensive.)
"That is a black, expensive handbag," would suggest that the emphasis is on "black" as opposed to on "expensive." (i.e. That is an expensive handbag, which is also black.)
Adding the word "new" results in this:
"That is a new, expensive, black handbag." Said otherwise: That is an expensive, black handbag which is new.
"That is an expensive, black, new handbag." Said otherwise: That is a black, new handbag which is expensive.
Try them out, putting the adjective you wish to emphasize in the first position. If it sounds wrong (and it might), try rewording the sentence entirely.
That handbag is expensive. It is also black and new.
That new, black handbag is expensive.
That expensive, black handbag is new.
That black handbag is both new and expensive.
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