Columbia University's board of trustees met late last night with a faculty steering committee to consider a complete reorganization of the university's power structure.

The steering committee--whose members include Daniel Bell, Lionel Trilling, and Walter Metzger--conferred late yesterday afternoon with student leaders, who asked for faculty and student control of the university's policy-making apparatus, to replace administration and board of trustees.

In a statement released at midnight by the Columbia student council, representing every major student organization, other demands were made. They include:

* The resignation of President Grayson Kirk and Vice President David Truman.

* The dropping of charges against the 720 demonstrators arrested yesterday.

* The removal of police from the campus.

Columbia College officials cancelled classes for the remainder of the week. Student leaders had previously called for a strike. Classes have not been held since April 25.

More Violence

Meanwhile, more violence erupted between police and students. Three students suffered head lacerations after a clash with police inside the university gates. Thirty police and an equal number of students were involved in the melee, according to the Associated Press.

Later last night, 400 Negroes, in sympathy with the students, marched from Harlem to Columbia's gates, carrying such signs as, "Now you know why we hate the cops!"

Stony Brook

On the Stony Brook, Long Island, campus of the State University, 22 students seized control of the business office, demanding that Suffolk County police be removed from their campus. Suffolk police arrested 33 Stony Brook students last January in a drug raid.