You cannot do this. But if your more focused on downtime then cost, you maybe able to clone your main instance, mount a larger EBS storage device to your system, copy the data over and then redirect traffic to your new instance.
If you want, a method I use lately use S3 has a medium of backups and deployment to other systems. So for example, you have your existing system running..set a script to upload your data to s3 every N minutes/hours/days..then write a script to use when launching new instances to download that data. If your data isn't something like constantly updated then this should work fine(for me, I use this to distribute updated version of my codebase while the data itself is managed on a ec2 database server).
Hope that helps.
