Type ratings are fairly simple, there is no limit on how many you can have.
The time and cost involved varies with the amount of differences.
Basically you spend some time in the classroom studying differences and then spend some time in the air with an instructor who will then sign your logbook to say that you are competant on type. You can use it immediately but you need to take your logbook and licence into the CAA office to get it added to your licence at the first reasonable opportunity.
If you already fly a C172 it will be quick and easy to add a C182 for example because the only significant differences are the VP prop, weight and balance and a tad less tendency to float in ground effect. The next step from C182 to C206 is also simple.
Going from a C172 to a Baron is going to be a lot harder and more expensive, you will almost certainly have to convert to the Bonansa first.