Hi Fiona
How the subsequent signup behaves depends on the Signup workflow settings
You can 'Restrict subsequent signups' according to the status of the previous signup including the fully attended status
It is also possible to restrict the number of subsequent signups to allow someone to signup for more than one event.
If the setting 'Clear expired waitlis' is enabled then this will allow a user to signup to another event when the first event has started.
This should allow you to get the desired results for how you want the signup for multiple events to behave.
Regards