You can certainly create a new (larger) Persistent Disk and attach it to your instance as a data disk. This is a very good option, since it keeps your website data separate from your operating system. See the Persistent Disk docs for details on all the options.
In your case:
- Create a new Persistent Disk for the data. Pick a size large enough for your data and large enough to get the I/O throughput you want. (See this chart for details)
- Attach the disk to your instance.