Chiral magnetic phases with an unconventional topological twist in the magnetization are of huge interest due to their potential in spintronics applications. Here, we present a general method to induce such exotic magnetic phases using interfacial phase frustration within artificially grown superlattices. To demonstrate our method, we consider a multilayer with two different chiral magnetic phases as the competing orders at the top and bottom and show, using Monte Carlo calculations, that the interfacial phase frustration is realized at the central layer. In particular, we obtain three unconventional phases: a checkerboard skyrmion crystal, an incommensurate skyrmion stripe, and a ferrimagnetic skyrmion crystal. In these frustration-induced phases, the spin chirality driven topological Hall conductivity can be largely enhanced. This method provides a playground to realize unconventional magnetic phases in any family of materials that can be grown in superlattices.