Recognising the limit.
THE SIGNS
Queries consistently slow despite indexes and caching Connection limits reached regularly Backups and imports timing out routinely The database running into hundreds of megabytes or more with genuine content Concurrent writes causing lock contention
WHAT TO TRY FIRST
Caching, including object caching where available Cleaning bloat, which frequently removes most of the size Adding indexes on slow queries Reducing queries per page
Most sites that appear to have outgrown shared hosting have a fixable problem instead.
WHEN IT IS GENUINE
A busy shop with years of orders, substantial concurrent traffic, and a database that is genuinely large after cleaning.
At that point dedicated resources are appropriate.
WHAT CHANGES ON A VPS
You control the database configuration: buffer sizes, connection limits, query cache.
You also become responsible for tuning, backups and updates.
BEFORE MOVING
Open a ticket with your situation. We will tell you honestly whether it is a tuning problem or a capacity one.
We would rather fix the former than sell you the latter.