Due to the aging of our society, patient care needs to be well coordinated within the health care team in order to effectively manage the overall health of each patient. Staff nurses, as the patient's “ever-present” health care team members, play a vital role in the care coordination. The recently developed Nurse Care Coordination Instrument (NCCI) is the first of its kind that enables quantitative data to be collected to measure various aspects of nurse care coordination. Driven by this new development, we propose a multi-response multilevel model with joint fixed effect selection and joint random effect selection across multiple responses. This model is particularly suitable for modeling the unique data structure of the NCCI due to its ability of jointly modeling of multilevel predictors, including demographic and workload variables at the individual/nurse level and characteristics of the practice environment at the unit level and multiple response variables that measure the key components of nurse care coordination. We develop a Block Coordinate Descent algorithm integrated with an Expectation-Maximization framework for model estimation. Asymptotic properties are derived. Finally, we present an application to a data set collected across four U.S. hospitals using the NCCI and discuss implications of the findings.