Controversy surrounds the apparent rising maximums of morphological complexity during eukaryotic evolution, with organisms increasing the number and nestedness of developmental areas as evidenced by morphological elaborations reflecting area boundaries. No "predictable drive" to increase this sort of complexity has been reported. Recent genetic data and theory in the general area of gene dosage effects has engendered a robust "gene balance hypothesis," with a theoretical base that makes specific predictions as to gene content changes following different types of gene duplication. Genomic data from both chordate and angiosperm genomes fit these predictions: Each type of duplication provides a one-way injection of a biased set of genes into the gene pool. Tetraploidies and balanced segments inject bias for those genes whose products are the subunits of the most complex biological machines or cascades, like transcription factors (TFs) and proteasome core proteins. Most duplicate genes are removed after tetraploidy. Genic balance is maintained by not removing those genes that are dose-sensitive, which tends to leave duplicate "functional modules" as the indirect products (spandrels) of purifying selection. Functional modules are the likely precursors of coadapted gene complexes, a unit of natural selection. The result is a predictable drive mechanism where "drive" is used rigorously, as in "meiotic drive." Rising morphological gain is expected given a supply of duplicate functional modules. All flowering plants have survived at least three large-scale duplications/diploidizations over the last 300 million years (Myr). An equivalent period of tetraploidy and body plan evolution may have ended for animals 500 million years ago (Mya). We argue that "balanced gene drive" is a sufficient explanation for the trend that the maximums of morphological complexity have gone up, and not down, in both plant and animal eukaryotic lineages.