Observation of counterfactual intermediate responses, and evaluation of them as candidate surrogates, is complicated in a standard randomized trial as half of the responses are systematically missing by design. Although some augmentation procedures exist for obtaining counterfactual responses, they are specific to vaccine trials. We outline extensions to the existing augmentations and suggest augmentations of three trial designs outside the setting of vaccines. We outline the assumptions needed to identify the causal estimands of interest under each augmented design, under which standard likelihood-based methods can be used to evaluate intermediate responses as principal surrogates. Two of these designs, crossover and individual stepped-wedge, allow for the observation of clinical endpoints under both treatment and control for some subset of subjects and can therefore improve efficiency over standard parallel trial designs. The third, the treatment run-in design, allows for the observation of a baseline measure that may be as useful a surrogate as the true counterfactual intermediate response. As the evaluation methods rely on several assumptions, we also outline a remediation analysis, which can be used to help overcome assumption violations. We illustrate our suggested methods in an example from a drug-resistant tuberculosis treatment trial.