There is increasing interest in dual-agent dose finding trials, especially in oncology research. In recent years, various dual-agent dose escalation designs, including both model-based and rule-based trial designs, have been proposed. The performance of these methods depends on the pattern of the underlying toxicities. We developed two novel dual-agent dose escalation methods: Combo mTPI and mTPI+PIPE. Our proposed methods make escalation/de-escalation decisions according to the mTPI decision table and recommend dose level combinations for the next cohort according to pre-specified rules. The performance of our two proposed methods was compared with BLRM and PIPE in simulation studies under different dose-toxicity models. Overall, our methods demonstrated more stable performance across scenarios. Furthermore, the proposed methods offer an intuitive approach to dual-agent dose escalation that can be easily understood by clinicians with straightforward implementation.