Accurate results for the photoionisation of the Si⁺ (3s²3p ²P⁰) ground state are reported for the photon energy region between the first two ionisation thresholds, Si²⁺ (3s² ¹S^e, 3s3p ³P⁰), at 750 and 540 AA. The cross section is dominated by the autoionised ³P⁰ np, nf (n>or=4) Rydberg series, whose shapes and oscillator strengths are drastically perturbed by the ¹P⁰ 4p ²S^e, ²D^e interlopers. These results are the first outcome of an elaborate calculation, based on a consistent LS multichannel description of the initial bound state and the final continua. The ejection of one valence electron is allowed for, together with flexible relaxation within the remaining valence shell, and possible monoexcitation into a near-spectroscopic orbital (3d, 4s, 4p). This extensive calculation (12 ionic states, up to 22 channels) is the first application of a new numerical approach combining the advantages of the R-matrix and the multichannel quantum defect (MQDT) theories.