While functional neuroimaging studies typically focus on a particular paradigm to investigate network connectivity, the human brain appears to possess an intrinsic "trait" architecture that is independent of any given paradigm. We have previously proposed the use of "cross-paradigm connectivity (CPC)" to quantify shared connectivity patterns across multiple paradigms and have demonstrated the utility of such measures in clinical studies. Here, using generalizability theory and connectome fingerprinting, we examined the reliability, stability, and individual identifiability of CPC in a group of highly-sampled healthy traveling subjects who received fMRI scans with a battery of five paradigms across multiple sites and days. Compared with single-paradigm connectivity matrices, the CPC matrices showed higher reliability in connectivity diversity, lower reliability in connectivity strength, higher stability, and higher individual identification accuracy. All of these assessments increased as a function of number of paradigms included in the CPC analysis. In comparisons involving different paradigm combinations and different brain atlases, we observed significantly higher reliability, stability, and identifiability for CPC matrices constructed from task-only data (versus those from both task and rest data), and higher identifiability but lower stability for CPC matrices constructed from the Power atlas (versus those from the AAL atlas). Moreover, we showed that multi-paradigm CPC matrices likely reflect the brain's "trait" structure that cannot be fully achieved from single-paradigm data, even with multiple runs. The present results provide evidence for the feasibility and utility of CPC in the study of functional "trait" networks and offer some methodological implications for future CPC studies.