Outside the Loman family, the characters of interest in the play are Charley, Charley's son (Bernard), and Willy's boss (Howard). 

Of these characters, Charley has the most lines in the play and the largest role in the action of the play. Charley is Willy's neighbor and, to some extent, competitor, but he is also Willy's benefactor. Willy turns to Charley for money on a weekly basis, yet will not accept a job that Charley offers him. Willy also continues to criticize and deride Charley despite Charley's generosity and friendship. 

This relationship offers some interesting material for an assessment of Willy's character. 

Bernard offers a similar insight into Biff's character. It is Bernard who raises questions about why Biff fails to make up his math class. It is also Bernard who tries to influence Biff and keep his friend from stealing and heading down the wrong path. 

What character of Death of Salesman outside the Loman family can I write about?

Willy's boss, Howard, is a character outside the Loman family you can write about. Howard attempts to be patient with Willy but ultimately fails. Though he is stern and direct with Willy in their interview, he does attempt to be sympathetic for a while. Willy, however, presses too far against Howard's good will and is fired. 

This scene is the only one featuring Howard, but in it we see an important truth about Willy. For all his bluster earlier in the play, Willy's incapacity as a salesman becomes clear. Willy complains and makes excuses, but Howard states the case simply. Willy is no longer capable of representing the company. 

The way that Willy wears down Howard's good will and even shouts at Howard demonstrates a general aspect of Willy's character. Willy is proud to a degree that is completely unjustified and this pride leads rather directly to his demise.