This....
Could an enlarged Albatross, presumably called the
Royal Albatross after the (2nd) largest of that species, with four Peregrine engines exceed the two-engined capabilities of the DC-3?
Quite possibly.
Trouble is it would not be competing with a DC-3 in original form. DC-3s used both Wright and P&W engines and went through several different engines of each type. Numbers I have used are for the 1937-38 versions.
Yanking the DH-Gypsy King engines and replacing them with Peregrines means that you have added the weight of the liquid cooling system/s and you need larger/heavier propellers.
Albatross already weighed 21,300lbs empty. Gross max weight was 29,500lbs. Maybe you can increase the gross weight without beefing up the landing gear and/or structure but increasing the power by over 50% is going to push some loads to the max or beyond.
Airliners did not have the same head room for G loads that bombers did let alone fighters. G loads also included the landing gear impact loads and loads in other aspects of flight (negative G loads in a wind gust).
Number of smaller planes traded higher power engines for less payload for shorter take-off runs, higher cruising speeds or better ability to handle mountain ranges. Some did beef up the structure to take full advantage of the extra power (higher payload).
As for the DC-3. they got somewhat (100-200hp) more powerful engines.
In the US Boeing was planning on a 4 engine airliner (B-17 wings), Douglas built the DC-4E (too big and sold to Japan) and Curtiss was building the CW-20 which later turned into the C-46 with a change in tail and change in engines.
original estimates, 23,090lbs empty, 36,000lbs loaded. Engines were either 1500hp or 1600hp for take-off and 1350hp max cruise.
30 passengers, 200mph cruise at 10,000ft. range not given.
Paying for a heavier, more expensive (4 liquid cooled engines and larger props) Albatross means you have to carry more passengers to pay for it and to pay for the higher operating expenses.