61.63 covers the requirements to add a category or class rating, but that's a different issue than logging flight time.

It's important to understand that flying the airplane, and logging the time, are completely different subjects. The best way to illustrate that, without breaking it down to detail, is that there are times when one can fly an airplane but not log the time, and there are times when one can fly the airplane, but log it in various ways. For example, one can be the pilot in command, and be able to log pilot in command time, but there are also times when one may be the pilot in command, but may only be able to log second in command time. There are also times when one may be the pilot in command, but may not be able to log any flight time. The reasons come down to the way in which the flight is conducted and the specifics of the operation: logging time isn't the same as flying the airplane.

One may get a add-on multi engine airplane land rating in the course of a few hours, but until the checkride, one can't log that few hours as pilot in command time, even if performing the duties of PIC under supervision. One can log it as instruction received, along with an endorsement from an authorized instructor. During the checkride, the examiner can't be the pilot in command; the student logs PIC for that time. After the student has obtained his or her multi-engine land class rating to go with his or her airplane category rating, then the door is open to logging PIC time under 61.51(e).

The multi-engine rating training is primarily focused on the question of asymmetrical thrust; how does the airplane fly with less thrust available, and what thrust remains, off-center (trying to turn the airplane). With that question comes airspeed and ground limitations: there's a point at which there is insufficient control available, when working against asymmetrical thrust, and the multi-engine rating is all about understanding where that point is and how it impacts operations. It also has to do with understanding how loss of an engine affects climb and other important issues. Consequently, most of the flying is no different, really, than what the student has already done, if (s)he has been flying single engine airplanes. Minimal time is usually taken to focus on the specifics of engine-out operation...but there's not really much training or much in the way of training programs to get better at flying the airplane, per se. The student is supposed to already be able to fly the airplane. The multi-engine training is simply focusing on a particular aspect of flying airplanes.

Today, students are hyper-focused on getting minimum hours and trotting off to the airplanes with as little qualification as possible, for that all-important seniority number. Traditionally, this is not how it worked. A student would find a VFR job, instructing or doing tours, etc, then eventually an IFR job. The fledgling pilot might fly jumpers or two banners or do aerial photography, etc. At some point (s)he would begin doing charter or ambulance or freight and begin working up and after two or three thousand hours, find a commuter or regional, and after a few thousand hours of that, look beyond. Today, students expect to get minimal training and go to an airline and never leave that environment. There is a LOT of material and experience left behind that's never obtained. I have run into pilots who are on their third or fourth job, including individuals flying on widebody equipment, who did not know or understand what latitude/longitude was, and could not find a coordinate on a chart. It's nearly incomprehensible that anyone could reach a point beyond student pilot and not have mastered this, but we live in a world of minimal qualification and automation where students learn to follow little magenta lines on computer screens, and little else.

The hardest part of learning to fly is paying for it, and it's become quite expensive.

In the case of your son, the least expensive course is going to be to knock out multi-rating as efficiently as possible (meaning the minimum time to get the rating AND learn the material ), to enable him to begin logging multi PIC.

While the 15 hour requirement might seem like a lot (in terms of expense, think of it in terms of the student; would you prefer that your son learn to fly multi-engine airplanes from someone who has no experience in multi-engine airplanes? The nature of instruction is that it's often provided by the least experienced people in the industry; low-time pilots trying to "build hours." Inexperience teaching inexperience; a heirarchy of learning with no experience to pass along. 15 hours sounds like a lot, but it's not much experience to have, to turn around and train other multi-engine pilots. It's simply provided as a bare-minum baseline requirement before an individual is allowed to begin teaching others to fly multi-engine equipment, having just barely learned to fly that equipment himself, or herself.

Buying one's way to the 25 hour requirement has traditionally been unnecessary, because fledgling pilots would gain their initial hours instructing or doing other jobs. Today, individuals want to get to the airlines without instructing or doing other work to gain experience, and so end up buying their flight time instead of earning it by working. Consequently, it can be expensive. Personally, I'd much rather see someone go out and get experience, but today the up-and-coming are often in too big a rush to run before they can walk, and to get to an airline. A poster here once opined that everybody ought to have some experience flying ratty airplanes in the ice and weather, and other experience-building elements in their background, but it's too often missing, with folks simply buying the time. The lay of the land today, I suppose.