One of the mysteries of the English language finally explained.
With another consideration; especially with a motive or intention other than, or in addition to, that professed.
Late 18th century. From post-classical Latin alio intuitu, lit. ‘with another consideration’ from classical Latin aliō, ablative of alius other + intuitū, ablative of intuitus consideration.
alio intuitu/ˌalɪəʊ ɪnˈtuːɪtjuː/
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