We report a study of the decays B-0 --> J/psiK((*)0) pi(+) pi(-), which involve the creation of a u(u) over bar or d(d) over bar quark pair in addition to a (b) over bar --> (c) over bar(c(s) over bar) decay. The data sample consists of 110 pb(-1) of p(p) over bar collisions at roots = 1.8 TeV collected by the CDF detector at the Fermilab Tevatron collider during 1992-1995. We measure the branching fractions to be B(B-0 --> J/psiK(*0) pi(+) pi(-)) = (6.6 +/- 1.9 +/- 1.1) X 10(-4) and B(B-0 --> J/psiK(0) pi(+) pi(-)) = (10.3 +/- 3.3 +/- 1.5) X 10(-4). Evidence is seen for contributions from psi(2S)K-(*)0, J/psiK(0) rho(0), J/psiK(*+) pi(-), and J/psiK(1)(1270).
