Consider two brands that want to jointly test alternate web experiences for their customers with an A/B test. Such collaborative tests are today enabled using third-party cookies, where each brand has information on the identity of visitors to another website, ensuring a consistent treatment experience. With the imminent elimination of third-party cookies, such A/B tests will become untenable. We propose a two-stage experimental design, where the two brands only need to agree on high-level aggregate parameters of the experiment to test the alternate experiences. Our design respects the privacy of customers. We propose an unbiased estimator of the Average Treatment Effect (ATE), and provide a way to use regression adjustment to improve this estimate. On real and simulated data, we show that the approach provides valid estimate of the ATE and is robust to the proportion of visitors overlapping across the brands. Our demonstration describes how a marketer can design such an experiment and analyze the results.