β-Fructofuranosidases can divert their hydrolytic activity towards transglycosylation for the synthesis of high value-added products, including prebiotic fructooligosaccharides (FOS). A directed evolution strategy has been employed to enhance the transferase rate of the β-fructofuranosidase (SoINV) from the Schwanniomyces occidentalis yeast for the production of β-(2→6)-linked FOS. To screen for transferase activity of the SoINV functionally expressed in Saccharomyces cerevisiae, a high-throughput screening protocol based on two colorimetric assays was validated (with coefficient of variance below 11%). Mutagenic libraries were constructed by error-prone PCR and clones showing higher glucose:fructose ratio with respect to the parental type were identified. Further analysis by anion-exchange chromatography coupled with pulsed amperometric detection helped to identify mutants with improved yields for the synthesis of β-(2→6) fructooligosaccharides. Selected mutants displayed transferase initial rates enhanced ~2-fold over parent type, reaching production levels up to 47 g/L after 48 h of reaction for the formation of 6-kestose.