'multi-' originates from Latin, specifically the word 'multus', where 'mult-' meant 'many'; 'class' originates from Latin, specifically the word 'classis', where 'class-' meant 'a division or group'.

'class' came into English via Old French 'classe' and Middle English 'classe' from Latin 'classis'; the combining prefix 'multi-' (from Latin 'multus') began to be used productively in Modern English to form compounds such as 'multi-class' (20th century, especially in technical contexts like statistics and computing).

Initially, Latin 'classis' referred to a division of citizens (e.g., for military or census purposes); over time it evolved to mean a group or category, and in modern usage combined with 'multi-' to mean 'involving many categories/classes'.