In short, so long as you have an available batch apex job slot available, you can send multiple Soapbox Mailer campaigns at the same time.
This, of course, brings up the obvious question: what is a "batch Apex job slot" and why does it matter to me?
In order to send emails, Soapbox Mailer processes all of the messages you send in a campaign in what are called batches. Batches, and the associated process for handling batches called "Batch Apex", is really just a way that Salesforce provides overload protection on its network. When records are processed in a batch, they run as soon as there is ample processing time in the network for them to be processed, which might be slightly delayed from real-time execution.
A group of batches working together is called a job.
For every Soapbox Mailer campaign you send, one job is created when you hit the Send button, and a variable number of batches is created within that one job in order to process all of your emails as efficiently as possible.
Since Soapbox Mailer lives within the Salesforce platform, its operations are governed by the aptly named "governor limits" within Salesforce. One of these governor limits provides a cap on the number of batch jobs that can be processed at any time: 5. So, theoretically, if you are not using any other apps that are creating batches, you could send 5 Soapbox Mailer campaigns at the same time, since each would take one batch job slot.
So, back to the short story. Typically speaking, yes, you can send multiple Soapbox Mailer campaigns at once, and at most, you can send up to 5 campaigns at the same time.