From 1889 to 1910, Remington Arms Co. was one of the biggest competitors for Parker Bros. In those 21 years Remington Arms Co. sold 134200 of their hammer doubles, 41194 A- to EEO-Grade hammerless doubles and 98508 K-quality hammerless doubles, far more guns than the Brothers P built from 1866 to 1942.
E.D. Fulford won the 1898 Grand American Handicap at live birds with a CEO-Grade Remington Hammerless Double. For 1906, Remington's pro William Heer carried the high average for the year 96.3% on 14,055 targets shooting a pair of Remington hammerless doubles.
The Gun Behind the Man, The American Field, Mar. 2, 1907.jpg
The real nail in the coffin for all North American doubles came in 1905 when Remington Arms Co. introduced their John M. Browning designed Remington Autoloading Shotgun (later Model 11). The Remington Autoloading Shotgun won the Grand American Handicap in 1907.
1907 GAH Winner, J.J. Blanks, The American Field, June 29, 1907.jpeg
Again in 1908 the Remington Autoloading Shotgun won the GAH.
In 1908 Remington Arms Co. introduced their John D. Pedersen designed Remington Repeating Shotgun (later Model 10). By the end of 1909 Marcellus Hartley Dodge, the owner of Remington Arms Co. saw that the future was with his John M. Browning and John D. Pedersen designed shotguns and in February 1910 sold their entire inventory of break-action guns to Norvell - Shapleigh Hardware Co. in St Louis.
Other than both being boxlock hammerless doubles there is no commonality between the Parker Bros. and Remington hammerless doubles.