Abstract: Many cancer therapies invoke multiple drugs given to patients simultaneously. However, most traditional methods developed so far are designed to search for the MTD for one drug with a fixed dose of other drugs present. Shortcomings of existing designs include: (1) ignoring the information on the severity of the toxicities by using dichotomous outcome; (2) focusing on a single drug only; and (3) not taking into account the correlation between toxicities. The pre-specified dose levels of the two drugs of interest form a dose combination grid. Our goal is to estimate the MTD boundary on the dose combination grid taking into account correlations between toxicities. We assume that these two drugs have pharmacological toxicity synergistic effects and the toxicity monotonicity in both directions of the dose levels of the two drugs. Different escalation schemes and a skipping strategy using level curve approach are studied. A Bayesian multivariate Probit regression for correlated ordinal data and MCMC algorithms are used to search the MTD boundary adaptively. An empirical Bayesian credible region is obtained after the MTD boundary is estimated.