Sure, multiple capacitors are hooked in parallel all the time in circuits, and they get charged and discharged at the same time in parallel. A good example is at the output of a power supply circuit, where you will typically parallel "bulk" electrolytic capacitors (large value) and several smaller ceramic high frequency capacitors. That gives energy storage across a range of frequencies (low frequencies for the large "bulk" caps, and higher frequency decoupling by the smaller value ceramic caps).
If the capacitors are isolated from the charging source by resistors, then each branch will charge and discharge according to their RC time constants.