A series of 4H-chromenes containing various modifications in the ring B and polyalkoxy substituents in the ring E has been synthesized by Knoevenagel-Michael-hetero-Thorpe-Ziegler three-component domino reaction with the overall yield of 45-82%. The targeted molecules were evaluated in a phenotypic sea urchin embryo assay for antimitotic and microtubule destabilizing activity. The most active compounds 5{1,5} and 5{5,5} featured sesamol-derived ring B and m-methoxyphenyl or m-methoxymethylenedioxyphenyl ring E. Compounds 5{3,1}, 5{1,2}, 5{5,4}, 5{1,5}, and 5{5,5} exhibited strong cytotoxicity in the NCI60 human tumor cell line anticancer drug screen. Surprisingly, cell growth inhibition caused by these agents was more pronounced in the multidrug resistant NCI/ADR-RES cells than the parent OVCAR-8 cell line. The results suggest that polyalkoxy substited 4H-chromenes may prove to be advantageous for further design as anticancer agents.