Continuous precipitation coupled with continuous tangential flow filtration is a cost-effective alternative for the capture of recombinant antibodies from crude cell culture supernatant. The removal of surge tanks between unit operations, by the adoption of tubular reactors, maintains a continuous harvest and mass flow of product with the advantage of a narrow residence time distribution (RTD). We developed a continuous process implementing two orthogonal precipitation methods, CaCl2 precipitation for removal of host-cell DNA and polyethylene glycol (PEG) for capturing the recombinant antibody, with no influence on the glycosylation profile. Our lab-scale prototype consisting of two tubular reactors and two stages of tangential flow microfiltration was continuously operated for up to 8 days in a truly continuous fashion and without any product flow interruption, both as a stand-alone capture and as an integrated perfusion-capture. Furthermore, we explored the use of a negatively charged membrane adsorber for flow-through anion exchange as first polishing step. We obtained a product recovery of approximately 80% and constant product quality, with more than two logarithmic reduction values (LRVs) for both host-cell proteins and host-cell DNA by the combination of the precipitation-based capture and the first polishing step.