In this study, we propose a novel, high-conductivity multi-channel heterostructure based on lattice-matched InAlN/GaN channels with modulation-doping-induced two-dimensional electron gases (2DEGs). To facilitate device processing, the channel period thickness was minimized while maintaining a high electron mobility in each channel. We demonstrate a 10-channel heterostructure with a period thickness of 14 nm and a total sheet resistance of 82 omega (-1). By increasing the doping concentration in each channel, much higher carrier densities per channel were achieved, resulting in an ultra-low sheet resistance of 36 omega (-1). Furthermore, optimizing the heterostructure design enabled high electron mobilities, up to 1530 cm(2) V-1 s(-1), independent of the number of channels, by secluding the 2DEG from the barrier interfaces in each channel to avoid both strong interface roughness and ionized impurity scattering. This was achieved by modulation-doping of the GaN channel and the insertion of a GaN interlayer between the InAlN barrier and the AlN spacer. This approach offers a new platform for designing high conductivity heterostructures, where the general trade-off between electron mobility and carrier density can be significantly alleviated.