We have tested the scalability of three supercomputers: the Tianhe-2, Stampede and CS-Storm with multiscale fluid-platelet simulations, in which a highly-resolved and efficient numerical model for nanoscale biophysics of platelets in microscale viscous biofluids is considered. Three experiments involving varying problem sizes were performed: Exp-S: 680,718-particle single-platelet; Exp-M: 2,722,872-particle 4-platelet; and Exp-L: 10,891,488-particle 16-platelet. Our implementations of multiple time-stepping (MTS) algorithm improved the performance of single time-stepping (STS) in all experiments. Using MTS, our model achieved the following simulation rates: 12.5, 25.0, 35.5 μs/day for Exp-S and 9.09, 6.25, 14.29 μs/day for Exp-M on Tianhe-2, CS-Storm 16-K80 and Stampede K20. The best rate for Exp-L was 6.25 μs/day for Stampede. Utilizing current advanced HPC resources, the simulation rates achieved by our algorithms bring within reach performing complex multiscale simulations for solving vexing problems at the interface of biology and engineering, such as thrombosis in blood flow which combines millisecond-scale hematology with microscale blood flow at resolutions of micro-to-nanoscale cellular components of platelets. This study of testing the performance characteristics of supercomputers with advanced computational algorithms that offer optimal trade-off to achieve enhanced computational performance serves to demonstrate that such simulations are feasible with currently available HPC resources.