Assessing the agreement between an established and a new measurement system is a practical and important challenge in many application areas. The probability of agreement (PoA) has recently been introduced as a metric to assess such agreement when repeatability, the precision of the measurement system itself, represents the overall measurement system variation. However, it is common in practice for the measurement system to be operated by multiple individuals, and their effects can be an important part of the overall variation. Reproducibility represents the measurement variability attributable to different operators. This paper extends the PoA methodology to account for both the repeatability and reproducibility of each measurement system along with the relative bias between them. The developed methodology also allows imbalanced replicate measurements across operators and systems, while the operator effects can either be fixed or random. We use maximum likelihood estimation to estimate the PoA. The proposed approach is illustrated using two case studies. In the first one, we compare the agreement between an old and a new measurement system used for quality inspections in an industrial context. The second case study which is presented in Supplementary Materials file assesses the agreement between two devices used to measure respiratory rates.