Many close-in extrasolar planetary systems appear coplanar, as in our Solar system. However, mutual orbital inclinations and large stellar obliquities are common, the origin of which remains mysterious. Competing hypotheses to explain these misaligned architectures include perturbations from the quadrupolar potential of the host star, and perturbations from exterior giant planets. However, degeneracies in these hypotheses persist owing to a lack of information regarding such exterior giants. Recent findings suggest that giants residing exterior to compact planetary systems typically possess orbits inclined by about 10 degrees. Greater misalignments persist exterior to single-transiting systems, suggesting that external giants might destabilise systems of multiple super Earths, but only if the giant’s orbit is primordially misaligned. In this work, we show that primordial misalignments between the inner and outer components of planetary systems come about naturally, by way of a novel, synergistic dynamical interaction between the quadrupolar potential of the host star, and the secular influence of an exterior giant. More surprisingly, we find that exterior giant planets can either constitute a stabilising or a destabilising influence, depending upon the evolution of the host star. Our work brings up testable predictions relating transit multiplicity and exterior giant planetary orbits.