Phase I dose-escalation studies for a single-agent and combination of anti-cancer agents have explored various model-based designs to guide identification of a maximum tolerated dose and recommended phase II dose. This work describes a parallel approach to dose escalation to expedite identification of maximum tolerated doses both for an anti-cancer agent as monotherapy and in combination with another agent. We develop a three-parameter Bayesian logistic regression model that allows for more efficient use of information between monotherapy and combination parts of the study. The model allows the monotherapy and combination data to drive dose escalation of the combination of treatments, reflecting the known dose-toxicity relationship between the monotherapy and combination setting. Through a thorough simulation study in which the proposed model is compared to two comparative approaches, the three-parameter Bayesian logistic regression model is shown to accurately select doses in the target toxicity interval, performing similar to comparative approaches in terms of proportion of target dose/combination selection, while more than halving the proportion of doses selected that were greater than the target toxicity, thereby improving safety concerns.