Designing effective reward functions remains a central challenge in reinforcement learning, especially in multi-objective environments. In this work, we propose Multi-Objective Reward Shaping with Exploration (MORSE), a general framework that automatically combines multiple human-designed heuristic rewards into a unified reward function. MORSE formulates the shaping process as a bi-level optimization problem: the inner loop trains a policy to maximize the current shaped reward, while the outer loop updates the reward function to optimize task performance. To encourage exploration in the reward space and avoid suboptimal local minima, MORSE introduces stochasticity into the shaping process, injecting noise guided by task performance and the prediction error of a fixed, randomly initialized neural network. Experimental results in MuJoCo and Isaac Sim environments show that MORSE effectively balances multiple objectives across various robotic tasks, achieving task performance comparable to those obtained with manually tuned reward functions.