We investigate high dimensional modulation formats for multi-core fibers (MCFs) and spatial superchannels. We show that the low skew variations between MCF cores maybe exploited to generate 'multi-core' formats that offer significant advantages over independently transmitting conventional 4-dimensional formats in each core. We describe how pulse position modulation formats may be transposed to the spatial domain and then investigate a family of modulation formats referred to as core-coding, one of which has the same power and spectral efficiency as polarization switched quaternary phase shift keying but with half of the optical power, potentially improving non-linear tolerance for long distance transmission, albeit at the cost of implementation challenges. Finally, we investigate the application of set-partitioning to multi-core formats using a single-parity check bit transmitted in one quadrature of one polarization in one of the cores and polarization-division multiplexing quadrature phase shift keying data in all remaining cores. We observe that for high core counts, an advantage of almost 3 dB in asymptotic power efficiency may be obtained with negligible impact on spectral efficiency, which translates into experimentally measured reduction in the required optical signal-to-noise ratio of up to 1.8 dB at a bit-error-rate of 10-5 and the same data-rate, and additional transmission reach of up to 20%.