Team of Rivals not a Nest of Vipers

Joe Biden has said he wants a diverse set of viewpoints in his cabinet so he is vetting Republicans for appointees. I imagine this is influenced by Lincoln’s legendary ‘Team of Rivals’ and the book of the same name by Doris Goodwin published in 2005. Certainly I’ve seen Lincoln name checked by supporters of this policy move. However there’s a key distinction being missed by most, Seward and Chase were rivals of Lincoln, who were from his own party, the Republicans of that time.