The spectra of the trans-Neptunian dwarf planets (136472) Makemake and (136199) Eris are dominated by absorption bands of volatile CH4 (methane) ice (e.g., Brown et al., 2005; Licandro et al., 2006). Prior work has identified shifts in the CH4 band centers, which is indicative of CH4 in solution with volatile N2 (e.g., Tegler et al., 2008, 2010). Direct detection of N2 is challenging due to the overtone absorption feature of N2 at 2.15 μm being located in the wing of the strong 2.20 μm CH4 band. The presence of CO (carbon monoxide) ice has yet to be evaluated on either dwarf planet, either directly or indirectly. However, recent laboratory work by Tegler et al. (2019) identified a combination band of N2 and CO at 2.239 μm that could allow direct detection of both ices in the spectra of Makemake and Eris. This band was confirmed in the spectrum of Triton, an object with previous direct detections of both N2 and CO. In this investigation, we analyzed near-infrared spectra of Makemake and Eris obtained with the LUCI1 and LUCI2 spectrographs on the Large Binocular Telescope (LBT). These spectra cover 2.05 to 2.37 μm at a resolving power of ~6700, sufficient for evaluating the presence of the 2.239 μm N2:CO combination feature. We present the results of this analysis and discuss the implications for the surface compositions and potential seasonal atmospheres of Makemake and Eris.