When interviewing for a new account management job, it's imperative that you know which accounts you will be working on. Your client base will be a strong factor in determining your ultimate job satisfaction.
Not only should you know the accounts you'll work on, you should also ask the total number of different clients you'll be looking after. There is a vast difference between working with one client to working with three clients, or 15 clients.
The number of clients you end up working with will depend on a variety of factors, including:
It is both normal and expected that a large agency (such as a multi-national) will choose to work for large accounts with substantial campaigns and high demands. It is not unheard of for those types of accounts to have a dedicated client service team numbering 5 or more people.
In a large agency, a junior may still work as client service support across more than one team. The more senior you climb, the more likely you are to concentrate on one client - until you reach GAD (Group Account Director) level where you will assume oversight over multiple accounts.
An Account Manager within a mid to large-sized agency will, most likely, work across a small handful of clients. It is also likely that the team structure will see more than one person working across each account (e.g. AD/AM/AE).
Smaller agencies my not be able or willing to chase the big campaign-based accounts, so work will come into the agency on a project-by-project basis.
To ensure the client service team is fully-occupied and able to maximise revenue, it is highly plausible that each intermediate to senior account manager could look after many clients (10 or more is quite normal).
Some of these clients will supply regular work, others will appear once-in-a-blue-moon. In situations like this the Account Manager becomes a "juggler". Like all juggling acts, dropping a ball is more a case of "when" than "if"...but, if you are good, you'll learn to juggle remarkably well!
There is no correct answer to the question of whether it is "better" to work with one client or many - the wise Account Manager will ensure they experience both! Each option has pros and cons. Each will give you fantastic experience, and help to shape a well-rounded career.