The shape of coherent SiGe islands epitaxially grown on pit-patterned Si(001) substrates displays very uniform collective oscillations with increasing Ge deposition, transforming cyclically between shallower ''dome'' and steeper ''barn'' morphologies. Correspondingly, the average Ge content in the alloyed islands also displays an oscillatory behavior, superimposed on a progressive Si enrichment with increasing size. We show that such a growth mode, remarkably different from the flat-substrate case, allows the islands to keep growing in size while avoiding plastic relaxation.