Eight Gates Limits
Academy Students- 0
Genin- No more than 3 gates.
Chuunin- No more than 5 gates.
Jounin- Access to all 6 gates.
Sannin- Access to all 7-8 gates.
Kage- Access to all 8 gates.
Missing-Nin- Access to all 7 gates.
Akatsuki- Access to all 8 gates.
if you want to open more then what you can start out with then you need to train with a person that can open the gate that you want to open