March slots (simultaneous marches) start at 1 and cap at 6 total. Free path via Academy research (+4 max, all one-time, no ongoing cost once researched): Military > Formation (requires Academy Lv6) +1; Military > Adv Dispatch (requires Academy Lv13) +1; Military > Super Adv Dispatch (requires Academy Lv25) +1; Military Advance > Legion Expansion (requires Academy Lv35) +1. VIP path: reaching VIP level 5+ AND spending/activating a VIP time item grants +1 march slot while VIP time is active; this bonus does not increase further at any higher VIP level (even VIP20+), it is capped at a flat +1. So the practical maximum is 1 (base) + 4 (research) + 1 (VIP) = 6 march slots.
Original research source: Evony Guide Wiki