Robots can perform multiple tasks in parallel. This work is about leveraging this capability in automating multilateral surgical subtasks. In particular, we explore, in a simulation study, the benefits of considering this parallelism capability in developing execution models for autonomous robotic surgery. We apply our work to two surgical subtask categories: (i) coupled-motion subtasks, where multiple robot arms share the same resources to perform the subtask, and (ii) decoupled-motion subtasks, where each robot arm executes its part of the task independently from the others. We propose and develop parallel execution models for the surgical debridement subtask, a representative of the first category, and the multi-throw suturing subtask, a representative of the second one. Comparing these parallel execution models to the state-of-the-art ones shows significant reductions in the subtasks completion time by at least 40%. In 20 trials, our results show that our proposed model for the surgical debridement subtask, that uses hierarchical concurrent state machines, provides a parallel execution framework that is efficient while greatly reducing collisions between the arms compared to a naive parallel execution model without coordination. We also show how applying parallelism can lead to execution models that go beyond the normal practice of human surgeons. We finally propose the notion of “automation for surgical manual execution” where we argue that autonomous robotic surgery research can be used as a tool for surgeons to discover novel manual execution models that can significantly improve their surgical practice.