Multidisciplinary team (MDT) discussion is the gold standard in the management of interstitial lung disease (ILD). The rheumatologist is not routinely involved in MDT, even if up to 20% of ILD are related to systemic autoimmune rheumatic diseases (SARD). The study aims to assess the agreement and its variation over time between rheumatologists and pulmonologists in the screening of SARD and between rheumatologists and an MDT extended to rheumatologists (eMDT) in evaluating the progression of SARD. We computed the agreement between the pulmonologist and rheumatologist in the identification of red flags for SARDs of 81 ILD cases and between the rheumatologist alone and eMDT in the confirmation of 70 suspected SARD-ILD progressions. The agreement between rheumatologists and pulmonologists was moderate for the detection of autoimmunity test positivity (κ = 0.475, p < 0.001) and family history of SARD (κ = 0.491, p < 0.001) and fair for the identification of extrapulmonary symptoms (κ = 0.225, p = 0.064) or routine laboratory abnormalities consistent with SARD. The average agreement between the rheumatologist and eMDT in the identification of ILD progression was moderate (κ = 0.436, p < 0.001). The class of agreement improved from the first to the third semester. The average agreement with the rheumatologist ranged from fair to moderate, suggesting that a shared evaluation of SARD-ILD in eMDT could improve the diagnostic work-up and the evaluation of ILD progression.