The IceCube Neutrino Observatory is also a very unique extensive air shower (EAS) detector, that simultaneously measures the EAS footprint on the surface and the high-energy muons in deep ice. The surface array - IceTop, comprising of ice-Cherenkov tanks, will be enhanced in the coming years with scintillation detectors and radio antennas. The hybrid detection enables the reconstruction of EAS parameters based on different underlying signal distributions. A new framework within the IceCube software allows for a flexible implementation of signal and time models for different detector components and a combination of resulting likelihood functions. The in-ice muon signal can serve as an anchor for the reconstruction of the EAS axis, resulting in an improved reconstruction resolution. Moreover, it makes it possible to reconstruct EASs with an impact point outside the IceTop array, opening a larger zenith-angle range for analyses of IceTop and in-ice coincident events. In this contribution, we present the capabilities of the combined reconstruction for different classes of EAS events with various detector configurations.