Quick Answer
Standard mission maximum: 4 Operators.
Starting HQ capacity: 7 Operators. Documented HQ maximum: 20.
Permanent mission-cap increase: not documented in the official sources reviewed.
Special missions: additional controllable characters may be available.
Squad Size vs HQ Operator Capacity
Mission squad size counts deployed Operators; HQ capacity concerns the larger roster. A 20-Operator HQ does not mean 20 simultaneous mission slots.
Can You Increase Squad Size in Zero Company?
EA documents HQ expansion, but still describes a standard mission maximum of four. The reviewed official materials do not document a permanent deployment-cap upgrade. This is not a claim that one is impossible.
Can You Control More Than Four Characters?
Certain missions allow extra controllable characters. The Q&A does not specify their number or identify those missions; this is not evidence of permanent expansion.
How HQ Operator Capacity Works
Capacity can grow through The Den upgrades, story progression, and new Authored Operators joining. Exact upgrade costs and milestones are not specified in the cited answer.
What the planner represents
Plan a standard squad using four stable Builder slots. The planner does not simulate HQ capacity or mission-specific extra characters.