Yes, you can either do so in subdirectories or subdomains. How many of these do you anticipate setting up? If it's only a few, you can do what Patrick suggests and set them up individually. If you're going to have a lot of them, you might think about installing one of the multi-user installations of WordPress like The Lyceum Project or WordPress Mu.
Two cautionary notes:
1. With lots of plugins, WordPress can be demanding on server resources. This is multiplied by having multiple blogs.
2. As the account holder, you will be held responsible for the performance and content on the blogs hosted under your account. You will have to make sure the blogs are efficient enough to run under a shared hosting environment and you will have to make sure that people you give access to make sure that only legal content is hosted. Remember, it's your account that will get canceled if other people violate the Terms of Service. Be careful so you don't get burned!
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