Same used before a noun is always definite: the same X, or less commonly that/this/those/these same X. So one more same X is at least not idiomatic, and I'm not sure it's grammatical.
But it can be used independently, following the noun it qualifies, so
There must be one more piece the same as this.
is fine, and the normal way to express what you are trying to say.
Similarly, two same pieces is not normal, but two pieces the same is fine.
Your second case is problematical in a different way.
There must be one more piece of this.
is grammatical, but sounds odd in this context because a piece of normally means "a part of a whole", whereas I think you mean "a piece like this". You could also say "a piece of this type", or "a piece of this shape", and then the expressed "type" or "shape" would override the usual meaning of "a piece of".