There's also some pretty major long-term economic problems underlying the Crisis. The late Republic and early Principate had been financed largely by plunder of conquered territories and the discovery of some new silver mines. By the third century, the Empire has largely run out of good places to conquer and plunder and the silver mines are running dry, but the soldiers still want salaries and provisions and the folks back home still want bread and circuses, so Emperors in the late Principate took to debasing the coinage. Augustus's denarius, for instance, was nearly pure silver, but by the reign of Gallienius, the denarius was almost pure copper. Nominal prices were rising accordingly, but nominal payments by the Empire weren't, leading to disgruntled soldiers and plebes. To avoid the Crisis of the Third Century, you need to find a way for the Emperor to actually pay his bills rather than trying to inflate them away.
Diocletian eventually addressed the problems by reentering the Empire in the East where the tax base was concentrated enough to support the administration and military, and letting the poorer West fend for itself on a shoestring budget. It'd be difficult to get there without some sort of chaotic transitional period, though.
