Photonic molecules can realize complex optical energy modes that simulate states of matter and have application to quantum, linear, and nonlinear optical systems. To achieve their full potential, it is critical to scale the photonic molecule energy state complexity and provide flexible, controllable, stable, high-resolution energy state engineering with low power tuning mechanisms. In this work, we demonstrate a controllable, silicon nitride integrated photonic molecule, with three high-quality factor ring resonators strongly coupled to each other and individually actuated using ultralow-power thin-film lead zirconate titanate (PZT) tuning. The resulting six tunable supermodes can be fully controlled, including their degeneracy, location, and degree of splitting, and the PZT actuator design yields narrow PM energy state linewidths below 58 MHz without degradation as the resonance shifts, with over an order of magnitude improvement in resonance splitting-to-width ratio of 58, and power consumption of 90 nW per actuator, with a 1-dB photonic molecule loss. The strongly coupled PZT-controlled resonator design provides a high-degree of resolution and controllability in accessing the supermodes. Given the low loss of the silicon nitride platform from the visible to infrared and the three individual bus, six-port design, these results open the door to novel device designs and a wide range of applications including tunable lasers, high-order suppression ultranarrow-linewidth lasers, dispersion engineering, optical parametric oscillators, physics simulations, and atomic and quantum photonics.