New millimeter-wavelength observations indicate that the L1551 star-forming region may be more complex than previously thought. CO and CS maps of a nearly 1 deg2 region show that multiple outflows confuse the interpretation of the structure of the L1551/IRS 5 and HL/XZ Tau molecular outflows. A 8' (0.4 pc) long, collimated redshifted molecular ridge lies near the northern rim of the redshifted lobe of the L1551 CO outflow. Its position and orientation indicates that it may be an outflow associated with the 2' long HH-30 optical jet. This flow has a mass of only about 0.01 to 0.02 M., a 3 to 5 km s-1 radial velocity, a dynamic age between 10(4) and 10(5) yr, and a mechanical luminosity of 2 x 10(-3) L.. Based on the spatial and kinematic data, we propose that this feature is not part of the redshifted lobe of the L1551, but a separate outflow. We detected a new CO outflow, L1551W, 17' west and 1' south of IRS 5, about 10' north of the L1551/IRS 5 blueshifted lobe. This flow has a greater than 10 km s-1 wide redshifted line wing, and is either monopolar or its blue lobe is confused with the L1551/IRS 5 outflow. The total mass of gas in this outflow is estimated to be about 0.1 M.. The mechanical luminosity and dynamic age are 0.2 L. and 3 x 10(4) yr. There are no known young stellar objects or dense cloud cores near L1551W which might be the source of this outflow. It is possible that this flow originates from L1551NE, an embedded young stellar object near IRS 5. The L1551 molecular cloud may contain at least four molecular outflows, L1551/IRS 5, HL/XZ Tau, the HH-30 molecular jet, and L1551W. The first three flows are associated with optical jets and groups of Herbig-Haro objects, providing further evidence that molecular outflows, shock-excited HH objects, and optical jets are closely related phenomena.