Young Dimitris Sgouros, who knocked them dead in Carnegie Hall last week when he made his American debut with the National Symphony Orchestra, is not exactly dropping out of sight. He will perform with the NSO here in late June, open the University of Maryland Piano Festival with a recital on July 18, and give a mind-boggling program a few days earlier at the Newport Music Festival.

The American chapter of the Sgouros saga began when the boy's mother, Marianthi Sgouros, wrote to Stewart Gordon, director of the University of Maryland International Piano Festival and Competition, asking whether Sgouros could be allowed to compete, although he is only 12 and the minimum age for competitors is 16. After listening to an audition tape, Gordon decided to refuse, not only because Sgouros was so far under age but because it would be unfair to the other competitors. But he wrote back offering instead to have Sgouros give the festival's opening recital, and he also recommended the young pianist to several friends, including Mstislav Rostropovich. Sgouros was flown to Amsterdam to meet Rostropovich while the NSO was there on tour, and arrangements for his NSO appearances were made immediately.

Meanwhile, the general director of the Newport Music Festival, Mark P. Malkovich III, was spending days on a transcontinental phone line with a Greek interpreter, trying to book Sgouros for the festival, which has a distinguished list of American debuts to its credit, including Bella Davidovich and Tchaikovsky Competition winners Andre Gavrilov and Mikhail Platynov. The program, planned for July 15 in The Breakers (the Cornelius Vanderbilt mansion) is enough to bring tears to the eyes and blisters to the hands of any pianist: a group of Scarlatti sonatas, Beethoven's "Appassionata," Chopin's Andante Spianato and Grande Polonaise Brillante, Ravel's "Gaspard de la Nuit" and Balakirev's "Islamey." Except for the Scarlatti (which should answer some still open questions about the young pianist's subtlety, legato, phrasing of quiet passages, etc.), any one of these pieces might normally be the climax of a program. "Then," recalls Malkovich with awe in his voice, "he asked me, 'Would you like the Mephisto Waltz as an encore?' " Sgouros is beginning to sound a bit hyperactive, and those who want him to relax and learn the fine details of his art will not be reassured by the latest news.