Amending the claims during the PCT process
There are a couple of opportunities during the PCT process to adjust the claims, so you don't necessarily have to have your claims perfect when you file the PCT. However these processes are not quite as flexible as the process offered during US prosecution.
The claims (but nothing else) can be amended once using article 19 amendments (PCT art 19). These are due at the later of (1) 16 months from the priority date; or (2) 2 months after the ISR is sent (PCT r 46.1). Article 19 amendments are published when the PCT application is published.
The claims (and the description and drawings) can also be amended using article 34 amendments, but only if the applicant files a demand for international preliminary examination (PCT art 34). The demand is due at the later of (1) 3 months after the ISR is sent; or (2) 22 months from the priority date (PCT r 54bis). The amendments should generally be filed with the demand (otherwise the IPEA may not consider them), but there is no requirement for this. The IPEA should then examine the amendments in preparing the IPRP.
Filing continuations and divisionals
There is no PCT analogue of US continuations (or divisionals in the rest of the world). However continuations and divisionals can typically be filed off from the first application which enters the national phase.