The complex interplay of charge, spin, orbital, and lattice degrees of freedom governs emergent phases in quantum materials, making strain a powerful control parameter. Recent advances in freestanding layer techniques have enabled extreme strains of nearly 8%, opening access to novel and often unexpected electronic and magnetic phases. Here, using a density functional theory approach, we investigate the effect of direction-selective uniaxial strain on the prototypical Jahn-Teller system La1−xCaxMnO3 (x = 0.25). We find that different strain directions stabilize qualitatively distinct structural, charge, and orbital responses, rather than merely different strengths of the same phase. In particular, extreme uniaxial strain selectively induces cooperative Jahn-Teller, breathing-like, and site-selective modulations, thereby enabling previously inaccessible intertwined orders in manganites. These results establish direction-selective uniaxial strain as a powerful and selective route for engineering emergent phases in quantum materials.