The "general rule" (for lack of a better term) is that you "go up" on branch circuits, and "down" on feeders. Elzappr is correct in stating the "800 amp" rule. At 800 amps and above the ampacity of the wire has to match or exceed the OCP. Notice the NEC Handbook.
Table 210.24 summarizes the requirements for the size of conductors and the size of the overcurrent protection for branch circuits where two or more outlets are required. The first footnote also indicates that the wire sizes are for copper conductors. Section 210.3 indicates that branch-circuit conductors rated 15, 20, 30, 40, and 50 amperes must be protected at their ratings. Section 210.19(A) requires that branch-circuit conductors have an ampacity not less than the rating of the branch circuit and not less than the maximum load to be served. These specific requirements take precedence over 240.4(B), which applies generally.
Table 210.24 summarizes branch-circuit requirements of conductors, overcurrent protection, outlet devices, maximum load, and permissible load where two or more outlets are supplied.
If the branch circuit serves a fixture load and supplies two or more fixture outlets, 210.23 requires the branch circuit to have a specific ampere rating that is based on the rating of the overcurrent device, as stated in 210.3. Thus, if the circuit breaker that protects the branch circuit is rated 20 amperes, the conductors supplying this circuit must have an ampacity not less than 20 amperes.