Optimizing a molecule initially in a 6-31+g(d) basis set and then reoptimizing it in a 6-311+g(d) basis set may not yield exactly the same results as directly optimizing in 6-311+g(d). Basis set changes can affect the accuracy of calculations, and reoptimization may introduce subtle differences due to the altered starting geometry. It's recommended to directly optimize in the desired basis set for more accurate results.

I completely disagree with the previous answer. Preliminary geometry optimization using a “worst” basis is a standard recommended procedure in all quantum chemistry textbooks. In many cases, researchers using a "large" basis set perform only single-point calculations using previously obtained geometry to refine the energy and other characteristics.

I agree with Alexey N. Masliy . Not only starting with a simpler BS and subsequently use larger BS is a commonly adopted strategy, but it is often a good practice to start from a pre-optimized geometry obtained from structural data or even semiempirical optimized metric parameters. Of course it is recommended to verify the final optimized structure with a vibrational analysis.