Sargent holding "court" at his studio. To be painted by Sargent was to be painted by the best and come they did, lined up for their portraits, Royalty and society women each with their own footman.  

The Joke here was that Sargent absolutely hated the idea of "holding court" at his studio. The inevitable throng that would accompany a sitter proved time and again to be distracting. The expression on his face here, though you can't quite see it very well, is of utter befuddlement or shock. 
 

Sir Henry Maximilian Beerbohm, or "Max"  was a writer and caricaturist. He was born in London, and had a half-brother by the name of Sir Herbert Beerbohm Tree. In 1907 Sargent would sketch Tree's daughter.  According to the Hon. Evan Charteris, Max was one of Sargent's favorite writers -- the two, obviously, were good friends. 

Max studied at Oxford, and published his first volume of essays under the title The Works of Max Beerbohm (1896). In 1910 he married US actress Florence Kahn (d.1951), and went to live, except during the two World Wars, in Rapallo, Italy. His caricatures were collected in various volumes beginning with Twenty-five Gentlemen (1896), and Poet's Corner (1904). His best-known work was his only novel, Zuleika Dobson (1911), a parody of Oxford undergraduate life. 
(biography.com) 
  

John Singer Sargent 
 
Zuleika  
c. 1907 
(very probably named after Beerbohm's book) 

 
Viola Tree  
1907 
(a "mug" of Beerbohm's niece) 
 
 
 

Notes 

 
Sargent's Tite Street Studio 
Photo