Originally Posted by JohnBurke

The approved flight training program under 14 CFR 61.51(e)(1)(iv) is a program which is specifically approved for the purpose, such as a program for training someone in airline operations.

If you break 61.51(e)(1)(iv) down, it contains several requirements:

61.51(e)(1)(iv)(A): the person performing the duties of PIC must hold a commercial or ATP pilot certificate, appropriate to category and class: airplane, multi-engine land, or airplane, multi-engine sea)

AND

61.51(e)(1)(iv)(B): the person performing the duties of PIC must be undergoing an approved pilot in command training program (eg, airline type program).

It's the first requirement above, 61.51(e)(1)(iv)(A), which specifies that the person logging the time under 61.51(e)(1)(iv) must have a pilot certificate that is appropriate to both category (here, airplane) and class (here, multi-engine land or sea, as appropriate). Specific to your question, a person logging time under this regulation must already hold a multi-engine rating. Training toward the multi-engine rating is not pilot in command experience, even if it's part of an approved program. The requirement is category, and class. Category is airplane, and the class is multi engine (land, or sea).

It sounds like you're cherrypicking the regulation, meaning that you're looking to choose either 61.51(e)(1)(iv)(A) OR 61.51(e)(1)(iv)(B). If you read the regulation, both (A) AND (B) are requirements for logging time under 61.51(e)(1)(iv).