The mechanical fingerprint of cells is inherently linked to the structure of the cytoskeleton and can serve as a label-free marker for cell homeostasis or pathologic states. How cytoskeletal composition affects the physical response of cells to external loads has been intensively studied with a spectrum of techniques, yet quantitative and statistically powerful investigations in the form of titration assays are hampered by the low throughput of most available methods. In this study, we employ real-time deformability cytometry (RT-DC), a novel microfluidic tool to examine the effects of biochemically modified F-actin and microtubule stability and nuclear chromatin structure on cell deformation in a human leukemia cell line (HL60). The high throughput of our method facilitates extensive titration assays that allow for significance assessment of the observed effects and extraction of half-maximal concentrations for most of the applied reagents. We quantitatively show that integrity of the F-actin cortex and microtubule network dominate cell deformation on millisecond timescales probed with RT-DC. Drug-induced alterations in the nuclear chromatin structure were not found to consistently affect cell deformation. The sensitivity of the high-throughput cell mechanical measurements to the cytoskeletal modifications we present in this study opens up new possibilities for label-free dose-response assays of cytoskeletal modifications.