You already know what this is. The multi-engine add-on is $5,100, flown in a Piper Seminole, and it is a class rating added to the certificate you hold rather than a new certificate. No additional knowledge test. Ground work, a block of flying, an oral and a flight test. Most current pilots finish it in something like five to ten hours, and the spread comes down to currency and to how comfortable you already are with a constant speed propeller.
The syllabus is mostly about asymmetric thrust and the arithmetic behind it: Vmc and why it moves with weight, altitude and configuration, the drag penalty of a windmilling propeller, drift down, and the honest gap between the accelerate go and accelerate stop numbers on a warm day. The airplane flies pleasantly on two engines. The rating is about what you do in the seconds after one of them stops being useful.
For a Glendale pilot this is the shortest genuinely valuable thing left on the list. Twenty-five minutes down the 134, no relocating, no week off in the desert. Most people book it as a compressed block, consecutive mornings or a run of evenings, and we are open 9 AM to 9 PM seven days a week to make that work. Once you hold it the Seminole rents at $649 an hour, so currency afterwards is a straightforward matter.