You can hit as many times as you want, up to your CA limit. Some GMs houserule that if you accrue an additional CA from two weapons or a shield, that CA must be used for defence only. Its a good rule, IMO.
But remember that if you hit, hit hit then you really, really risk opening yourself up with no option to parry. If you have characters who want to concentrate completely on whacking the buggery out of an opponent at the expense of using CAs for defence, then they shouldn't complain if they get taken down pretty rapidly. If they're outnumbered, acting defensively and making use of different actions such as using weapon reach or over-extending an opponent through a defensive CA, become invaluable.