Unmeasured confounding, selection bias, and measurement error are well-known sources of bias in epidemiologic research. Methods for assessing these biases have their own limitations. Many quantitative sensitivity analysis approaches consider each type of bias individually, while more complex approaches are harder to implement or require numerous assumptions. By failing to consider multiple biases at once, researchers can underestimate -- or overestimate -- their joint impact. We show that it is possible to bound the total composite bias due to these three sources, and to use that bound to assess the sensitivity of a risk ratio to any combination of these biases. We derive bounds for the total composite bias under a variety of scenarios, providing researchers with tools to assess their total potential impact. We apply this technique to a study where unmeasured confounding and selection bias are both concerns, and to another study in which possible differential exposure misclassification and unmeasured confounding are concerns. We also show that a "multi-bias E-value" can describe the minimal strength of joint bias-parameter association necessary for an observed risk ratio to be compatible with a null causal effect (or with other pre-specified effect sizes). This may provide intuition about the relative impacts of each type of bias. The approach we describe is easy to implement with minimal assumptions, and we provide R functions to do so.