A combination drug product with two or more active compounds may be superior to each of its components with higher dose levels and, therefore, is preferred in terms of efficacy, cost, and safety. To study a combination drug, researchers often conduct trials by using a factorial design with combinations of dose levels of each drug component. By applying some bootstrap methods, we construct multiple testing procedures to simultaneously identify combinations superior to each drug component with any dose level. These multiple testing procedures are more powerful than Holm's step-down procedure that is known to be very conservative. When there is only one study endpoint, applying the bootstrap is straightforward. In many studies, however, there are two or more study endpoints and it is not simple to apply the bootstrap. We apply one version of the bootstrap and then use an upper bound to control the familywise error defined as the probability of rejecting at least one true null hypothesis. Properties of the bootstrap multiple testing procedures are discussed and examined in some simulation studies. Copyright © 2012 John Wiley & Sons, Ltd.