With most devices you can only have one wire per screw terminal, however, some breakers do support multiple wires under terminals. If the device allows multiple taps, it must be listed for the purpose.
110.14 Electrical Connections.
(A) Terminals. Connection of conductors to terminal parts shall ensure a thoroughly good connection without damaging the conductors
and shall be made by means of pressure connectors (including set-screw
type), solder lugs, or splices to flexible leads. Connection by means
of wire-binding screws or studs and nuts that have upturned lugs or
the equivalent shall be permitted for 10 AWG or smaller conductors.
Terminals for more than one conductor and terminals used to connect
aluminum shall be so identified.
Taps, Splices, and Feed Throughs
Feed throughs, taps, and splices are allowed, but only if they do not over fill the enclosure.
312.8 Enclosures for Switches or Overcurrent Devices. Enclosures for switches or overcurrent devices shall not be used as junction
boxes, auxiliary gutters, or raceways for conductors feeding through
or tapping off to other switches or overcurrent devices, unless
adequate space for this purpose is provided. The conductors shall not fill the wiring space at any cross section to more than 40 percent of the cross-sectional area of the space, and the conductors, splices, and taps shall not fill the wiring space at any cross section to more than 75 percent of the cross-sectional area of that space.
If you have no room for a new breaker in the panel, consider a Tandem Breaker. You'll have to check whether or not your panel supports them, but in some cases a tandem breaker can save you from having to install a new panel or a sub-panel.
In the 2008 version of the National Electrical Code (NEC), section 210.12 has been updated to require Arc-Fault Circuit-Interrupter (AFCI) protection in many areas of the home.
210.12 Arc-Fault Circuit-Interrupter Protection.
(B) Dwelling Units. All 120-volt, single phase, 15- and 20-ampere branch circuits supplying outlets installed in dwelling unit family
rooms, dining rooms, living rooms, parlors, libraries, dens, bedrooms,
sunrooms, recreation rooms, closets, hallways, or similar rooms or
areas shall be protected by a listed arc-fault circuit interrupter,
combination-type, installed to provide protection of the branch
Depending on the changes you're making to the wiring, the inspector may require you to update the breaker for this or all branch circuits feeding these areas. This decision will be completely up to the Authority Having Jurisdiction (AHJ), since it's a judgment call on whether or not you're making a large enough change to warrant the extra work.