Droplet microfluidics has become a standard technology for high throughput screening of monoclonal antibody (mAb)-producing cells due to high droplet single-cell confinement frequency and the rapid analysis and sorting of the cells of interest with their secreted mAbs. However, existing droplet-based devices are not compatible with many mAbs characterization assays. Typical antigen-binding assays depend on the co-compartmentalization of single B (or hybridoma) cells with target cells (or beads), which are usually inefficient due to Poisson statistics. The method creates undesired combinations of the two cells in each droplet, causing frequent losses of rare cells with the desired antigen-specificity. In addition, many mAbs characterization assays rely on a series of wash steps that require reagent removal and exchange which is not feasible in current droplet-based devices. In our work, we describe a new method for on-demand co-encapsulation of cells that eliminates the challenges described above. We have developed a droplet digital-based (D2) microfluidic device that allows for deterministic trapping of hybridoma cells with target cells with high efficiency and enables the washing and addition of fresh media. Our platform identifies hybridoma cells that are expressing antibodies of interest with the use of antibody-characterization assays to find rare-cell antibody candidates. A D2-device has a three-layer structure: an electrode layer patterned on a glass substrate, a dielectric, and a channel layer made of PDMS for droplet generation and manipulation as described in previous work. Our work represents the first microfluidic device that allows for such integration given the difficulties associated with washing in between consecutive steps inside the droplets and efficient co-encapsulation of hybridoma and target cells. We propose that such a platform enables an automated method for a broad range of mAbs characterization assays and identify and select rare cells producing specific antibodies.