This letter presents a system for manipulating microscale objects in an obstacle prone environment using push manipulations based on a learned model. The path planning is done using a RRT* search algorithm adapted for this setup and the manipulation is done using a regression model trained on manipulation data collected a priori . This model is used to capture the dynamics of the micropart and its interaction with the environment such as frictional contacts and other uncertainties that are difficult to model explicitly. The push manipulation is done using probes attached to micromanipulators capable of high-resolution movements. The setup is demonstrated through simulations using two manipulators and a LEGO inspired micropart as it is pushed through different trajectories. Experiments include performing push manipulations in the presence of obstacles, with single and multiple manipulators, and demonstrating the use of the system to perform a microassembly task. The major contribution is a working manipulation system for microparts that implicitly models difficult to model aspects like uncertainties in the environment, such as physical phenomena in the microscale like friction, and the contact interactions between microparts.