The phrase "extensively reading" is grammatically correct and can be used in written English.
It typically refers to someone reading a large amount of material or reading very deeply and thoroughly on a specific topic. Example: "In order to become a better writer, I have been extensively reading books on grammar and style."
Revisionist satire spurred Alice Randall to create The Wind Done Gone (2001), a parody of the 20th century's most extensively read historical novel, Margaret Mitchell's Gone with the Wind (1936).
Since the Bureau of Historiography was next to the Bureau of Statistics, he extensively read 213 original historical documents gathered to the Bureau of Historiography by that time, and compiled two books: food history of Japan and the disaster history of Japan.
He extensively read the works of Wilhelm von Humboldt, who had written on Mesoamerica, and started corresponding with the historian Washington Irving, the Swiss writer Sismondi and the French historian Jacques Nicolas Augustin Thierry.
I researched the disease extensively and read accounts of the survivors.
Hull is exhuming the ghost of its grumpy former librarian Philip Larkin, whose poetry is extensively quoted, read by the actor Sir Tom Courtenay, in a film supporting its bid.
After reading extensively about the history of the region, Ms. Papadopoulos drove for 12 hours to reach the Turkish border.
Subsequently he moved on to other scholar relatives, traveling from teacher to teacher in the traditional way and reading extensively in the Islamic sciences.
She was humiliated, bored, and regarded with suspicion while at court, but she found comfort in reading extensively and in preparing herself for her future role as sovereign.
She spent the winter of 1849 50 at Geneva, reading extensively while living with the family of François D'Albert Durade, who painted a portrait of her.
