By rapidly creating libraries of thousands of unique, miniaturized reactors, droplet microfluidics provides a powerful method for automating high-throughput chemical analysis. In order to engineer in-droplet assays, microfluidic devices must add reagents into droplets, remove fluid from droplets, and perform other necessary operations, each typically provided by a unique, specialized geometry. Unfortunately, modifying device performance or changing operations usually requires re-engineering the device among these specialized geometries, a time-consuming and costly process when optimizing in-droplet assays. To address this challenge in implementing droplet chemistry, we have developed the “K-channel,” which couples a cross-channel flow to the segmented droplet flow to enable a range of operations on passing droplets. K-channels perform reagent injection (0–100% of droplet volume), fluid extraction (0–50% of droplet volume), and droplet splitting (1:1–1:5 daughter droplet ratio). Instead of modifying device dimensions or channel configuration, adjusting external conditions, such as applied pressure and electric field, selects the K-channel process and tunes its magnitude. Finally, interfacing a device-embedded magnet allows selective capture of 96% of droplet-encapsulated superparamagnetic beads during 1:1 droplet splitting events at ~400 Hz. Addition of a second K-channel for injection (after the droplet splitting K-channel) enables integrated washing of magnetic beads within rapidly-moving droplets. Ultimately, the K-channel provides an exciting opportunity to perform many useful droplet operations across a range of magnitudes without requiring architectural modifications. Therefore, we envision the K-channel as a versatile, easy to use microfluidic component enabling diverse, in-droplet (bio)chemical manipulations.