Context. Protoplanetary disks contain structures such as gaps, rings, and spirals, which are thought to be produced by the interaction between the disk and embedded protoplanets. However, only a few planet candidates are found orbiting within protoplanetary disks, and most of them are being challenged as having been confused with disk features. Aims: The VLT/MUSE discovery of PDS 70 c demonstrated a powerful way of searching for still-forming protoplanets by targeting accretion signatures with medium-resolution integral field spectroscopy. We aim to discover more proto-planetary candidates with MUSE, with a secondary aim of improving the high-resolution spectral differential imaging (HRSDI) technique by analyzing the instrumental residuals of MUSE. Methods: We analyzed MUSE observations of five young stars with various apparent brightnesses and spectral types. We applied the HRSDI technique to perform high-contrast imaging. The detection limits were estimated using fake planet injections. Results: With a 30 min integration time, MUSE can reach 5ensuremathσ detection limits in apparent Hα line flux down to 10$^-14$ and 10$^-15$ erg s$^-1$ cm$^-2$ at 0.075 and 0.25'', respectively. In addition to PDS 70 b and c, we did not detect any clear accretion signatures in PDS 70, J1850-3147, and V1094 Sco down to 0.1. MUSE avoids the small sample statistics problem by measuring the noise characteristics in the spatial direction at multiple wavelengths. We detected two asymmetric atomic jets in HD 163296 with a very high spatial resolution (down to 8 au) and medium spectral resolution (R ~ 2500). Conclusions: The HRSDI technique when applied to MUSE data allows us to reach the photon noise limit at small separations (i.e., $łt$0.5’'). With the combination of high-contrast imaging and medium spectral resolution, MUSE can achieve fainter detection limits in apparent line flux than SPHERE/ZIMPOL by a factor of ~5. MUSE has some instrumental issues that limit the contrast that appear in cases with strong point sources, which can be either a spatial point source due to high Strehl observations or a spectral point source due to a high line-to-continuum ratio. We modified the HRSDI technique to better handle the instrumental artifacts and improve the detection limits. To avoid the instrumental effects altogether, we suggest faint young stars with relatively low Hα line-to-continuum ratio to be the most suitable targets for MUSE to search for potential protoplanets.