A method to reduce the Lehmer measure in a multi-term Machin-like formula for $\pi$

Previously we have proposed a new method of transforming quotients into integer reciprocals in the Machin-like formulas for $\pi$. As a further development, here we show how to generate a multi-term Machin-like formula for $\pi$ with a reduced Lehmer measure. The Mathematica codes validating these results are presented.