Microfluidics-based drug-screening systems have enabled efficient and high-throughput drug screening, but their routine uses in ordinary labs are limited due to the complexity involved in device fabrication and system setup. In this work, we report an easy-to-use and low-cost arbitrarily accessible 3D microfluidic device that can be easily adopted by various labs to perform combinatorial assays for high-throughput drug screening. The device is capable of precisely performing automatic and simultaneous reagent loading and aliquoting tasks and performing multistep assays with arbitrary sequences. The device is not intended to compete with other microfluidic technologies regarding ultra-low reaction volume. Instead, its freedom from tubing or pumping systems and easy operation makes it an ideal platform for routine high-throughput drug screening outside traditional microfluidic labs. The functionality and quantitative reliability of the 3D microfluidic device were demonstrated with a histone acetyltransferase-based drug-screening assay using the recombinant Plasmodium falciparum GCN5 enzyme, benchmarked with a traditional microtiter plate-based method. This arbitrarily accessible, multistep capable, low-cost, and easy-to-use device can be widely adopted in various combinatorial assays beyond high-throughput drug screening.