Actually, the B&A was a different kind of case. NYC leased the B&A in 1900 and, as in most lease situations, absorbed its equipment onto its own roster and started relettering things "NYC&HR." But there was a backlash in Boston, which never cottoned to those crude usurpers from New York in the first place, and the insensitive actions of the NYC&HR-appointed B&A general manager aggravated the situation more. As a result, NYC went back to using the B&A name on equipment and property. But it had every legal right tro use "NYC" any time it wanted, and by the late 1940s NYC steam and diesel power were common on the B&A.
In 1935-36 NYC leased the Big Four, Michigan Central, and some smaller fry after many years of frustration in trying to merge these lines. (The minority stockholders wanted too much, and after the LS&MS merger NYC decided that the effort was just too expensive.) At that time, all Big Four, MC, T&OC, etc. power was relettered NYC and renumbered in the NYC series.
More similar to the P&LE was the Peoria & Eastern, which also kept its identity into Penn Central.