In this paper, we experimentally demonstrate the performance of a non-orthogonal multi-band super-Nyquist carrier-less amplitude and phase (m-SCAP) modulation for visible light communications (VLC). We break the orthogonality between sub-bands in the frequency domain by compressing the spectrum, purposely overlapping them, and introducing inter-band interference (IBI). We demonstrate that our proposed system can tolerate IBI, and hence spectral efficiency can be increased without introducing additional complexity to the receiver. We show that m-SCAP can tolerate up to 30% and 20% compression for 4-and 16-level quadrature amplitude modulation, respectively, thus leading to an improvement in spectral efficiencies up to 40% and 25%, respectively, at the cost of bit error rate performance, which however remains below the 7% forward error correction limit. Moreover, the experimental results are supported by numerical simulations. Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.