Nos Fóruns do Dropbox , por uma pessoa de suporte do Dropbox:
Note that in the vast majority of cases where people are asking about multiple accounts is best solved by Shared Folders. Unless there are two different people using the same computer, which different OS accounts is the proper way of handling it. Third party applications and hacks that are designed to get multiple Dropbox instances running at the same time for one user is not recommended, not only because they are completely unsupported (by the Dropbox team at least), but also because Dropbox is not meant to be utilized in such a manner. So the chance of issues is a lot higher than running Dropbox as per normal.
As respostas para esta pergunta também podem ajudar você. O Dropbox suporta várias contas para várias contas de usuário na mesma máquina, mas uma das respostas permite que você faça isso sem precisar de vários usuários. Pode ser contra os Termos de Serviço.