An algebra A on a Hilbert space H is transitive if it contains the identity operator and has no invariant (closed) subspace other than the two trivial ones. The transitive algebra question asks: if A is a transitive algebra, is A strongly dense in B(H)? We proved that if a transitive algebra A is 2-fold transitive and A contains a standard finite von Neumann algebra, then A is strongly dense in B(H). This result extends William Arveson's classical result on transitive algebra question and partly answers a question of Arveson. Some interesting examples related to free probability theory will also be discussed.