Deep near-infrared photometric surveys are efficient in identifying high-redshift galaxies, however, they can be prone to systematic errors in photometric redshift. This is particularly salient when there is limited sampling of key spectral features of a galaxys spectral energy distribution (SED), such as for quiescent galaxies where the expected age-sensitive Balmer/4000 break enters the
K-band at z> 4. With single-filter sampling of this spectral feature, degeneracies between SED models and redshift emerge. A potential solution to this comes from splitting the Kband into multiple filters. We use simulations to show an optimal solution is to add two medium-band filters, Kblue ( cen = 2.06 m, = 0.25 m) and Kred ( cen = 2.31 m, = 0.27 m), that are complementary to the existing Ks filter. We test the impact of the K-band filters with simulated catalogs comprised of galaxies with varying ages and signal-to-noise. The results suggest that the K-band filters do improve photometric redshift constraints on z> 4 quiescent galaxies, increasing precision and reducing outliers by up to 90%. We find that the impact from the K-band filters depends on the signal-to-noise, the redshift, and the SED of the galaxy. The filters we designed were built and used to conduct a pilot of the FLAMINGOS-2 Extragalactic Near-Infrared K-band Split survey. While no new z> 4 quiescent galaxies are identified in the limited area pilot, the Kblue and Kred filters indicate strong Balmer/4000 breaks in existing candidates. Additionally, we identify galaxies with strong nebular emission lines, for which the K-band filters increase photometric redshift precision and in some cases indicate extreme star formation.