Synonyms for Large-hearted (same or very similar meaning)
WordNet sense 1 (showing or motivated by sympathy and understanding and generosity):
benevolent, charitable, kindly, openhearted, sympathetic, good-hearted
WordNet sense 2 (having or showing a tender and considerate and helpful nature; used especially of persons and their behavior):
kind
From the ODE community, based on WordNet
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