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Molecules and atomic highly charged ions provide powerful low-energy probes of the fundamental laws of physics: Polar molecules possess internal fields suitable to enhance fundamental symmetry violation by several orders of magnitudes, whereas atoms in high charge states can feature large relativistic effects and compressed level structures, ideally posed for high sensitivity to variations of fundamental constants. Polar, highly charged molecules could benefit from both: large internal fields and large relativistic effects. However, a high charge dramatically weakens chemical bonding and drives systems to the edge of Coulomb explosion. Herein, we propose multiply-charged polar molecules, that contain actinides, as promising candidates for precision tests of physics beyond the standard model. Explicitly, we predict PaF$^{3+}$ to be thermodynamically stable, coolable and well-suited for precision spectroscopy. The proposed class of compounds, especially with short-lived actinide isotopes from the territory of pear-shaped nuclei, has potential to advance our understanding of molecules under extreme conditions, to provide a window into unknown properties of atomic nuclei, and to boost developments in molecular precision spectroscopy in various areas, such as optical clocks and searches for new physics.