While much of the causal inference literature has focused on addressing internal validity biases, both internal and external validity are necessary for unbiased estimates in a target population of interest. However, few generalizability approaches exist for estimating causal quantities in a target population when the target population is not well-represented by a randomized study but is reflected when additionally incorporating observational data. To generalize to a target population represented by a union of these data, we propose a class of novel conditional cross-design synthesis estimators that combine randomized and observational data, while addressing their respective biases. The estimators include outcome regression, propensity weighting, and double robust approaches. All use the covariate overlap between the randomized and observational data to remove potential unmeasured confounding bias. We apply these methods to estimate the causal effect of managed care plans on health care spending among Medicaid beneficiaries in New York City.