To a certain extent, yes, depending what activity it is that you are talking about.
With respect to pets, you should know that in California, any governing documents (such as CC&Rs) modified after January 1, 2001 must allow pets.
California Civil Code section 1360.5(a)&(e) provides:
"No governing documents shall prohibit the owner of a separate interest within a common interest development from keeping at least one pet within the common interest development . . . This section shall become operative on January 1, 2001, and shall . . . apply to governing documents entered into, amended, or otherwise modified on or after that date. "
If you had three pets, and the new CC&Rs now limit each owner to two pets, but your pets were brought in before new restrictions were adopted, your three pets are automatically grandfathered and the HOA cannot force their removal. (See California Civil Code section 1360.5(c).)
Frank W. Chen has been licensed to practice law in California since 1988. The information presented here is general in nature and is not intended, nor should be construed, as legal advice. This posting does not create any attorney-client relationship with the author. For specific advice about your particular situation, consult your own attorney.