The phrase "another set of pieces" is correct and usable in written English.
It can be used when referring to an additional collection or group of items, components, or elements in various contexts.
Example: "After assembling the first model, I realized I needed another set of pieces to complete the project."
Alternatives: "an additional collection of items" or "a different group of components".
By the way, when the 50th anniversary of oral contraceptives rolls around this May, can you maybe consider coming up with some alternatives instead of writing another set of gushing fluff pieces about Margaret Sanger?
Mr. Gligoric learned to play chess when he was 11 and made his first set of pieces by carving the caps of wine corks.
An exception is a set of pieces by the Italian avant-garde composer Salvatore Sciarrino, who transcribed works from Gesualdo to Gershwin for saxophone quartet.
Once a student had read the complete set of pieces, she was given a surprise six-question quiz, with questions concerning both recollection and inference.
In 1994 she was approached by the Scottish Chamber Orchestra, which was commissioning a set of pieces on which composers would work with other artists from other disciplines.
The album is a set of pieces for drum set, gongs, electric guitar and electric bass, violin and viola, and in one case the single note of a piano.
The reflector's shape to be found is just a part of a set of pieces called in Lighting Engineering an optical set.
A new project looks to change that with a data set of pieces from great composers, annotated so the computers can follow along.
The next generation Lego Mindstorms improve on the original 1998 model of do-it-yourself robotics with a "32-bit NXT control brick, ultrasonic sensors, a revamped set of pieces, a new piece of visual programming software, and Bluetooth support".
One unpublished set of pieces, Kakehi ("Conduit"), written at the age of 17, incorporates the ryō, ritsu and insen scales throughout.
