Toluene is 114 octane, available at any hardware store. Might be a good stop-gap measure! Mix it with the 87 and you'll get to 93 quite easily.
However, I haven't researched it for our cars, so search a bit more to ensure it's safe. (Though it worked perfecty fine on my Stage 2.5 WRX STi)
'08 M3: AA G2L3, Catless X-Pipe & Sig Series Rear. AP rods. TC Kline EDC Coil Overs. MRF Alum Sub Frame Bushings. TMS Delrin Diff'l Bushings. BFI Motor Mounts. Recaro PP. BMW Perf Steering Wheel. P3 Gauge. PS Overflow Kit. APEX ARC-8 18"x9.5"/10.5". Conti Slicks 275/35F 305/30R. Stoptech Pads/SS Lines. Cantrell Brake Ducts.