Robot manipulation in cluttered scenes often requires contact-rich interactions with objects. It can be more economical to interact via non-prehensile actions, for example, push through other objects to get to the desired grasp pose, instead of deliberate prehensile rearrangement of the scene. For each object in a scene, depending on its properties, the robot may or may not be allowed to make contact with, tilt, or topple it. To ensure that these constraints are satisfied during non-prehensile interactions, a planner can query a physics-based simulator to evaluate the complex multi-body interactions caused by robot actions. Unfortunately, it is infeasible to query the simulator for thousands of actions that need to be evaluated in a typical planning problem as each simulation is time-consuming. In this work, we show that (i) manipulation tasks (specifically pick-and-place style tasks from a tabletop or a refrigerator) can often be solved by restricting robot-object interactions to adaptive motion primitives in a plan, (ii) these actions can be incorporated as subgoals within a multi-heuristic search framework, and (iii) limiting interactions to these actions can help reduce the time spent querying the simulator during planning by up to 40x in comparison to baseline algorithms. Our algorithm is evaluated in simulation and in the real-world on a PR2 robot using PyBullet as our physics-based simulator. Supplementary video: \url{https://youtu.be/ABQc7JbeJPM}.