Your needs can change as your website(s) evolve, and your current web hosting account might not fulfill your new needs. You can buy extras to your current account, upgrade to a more extensive package or find a web host more appropriate for your new website habits.
Account extras
An option is to buy extra disk space or whatever you need.
Common addons to a web hosting package are disk space, email addresses, data
transfer, sub domains, extra domains and (more) databases.
In general, the prices for extras are higher than the extra amount you have to
pay for a little more expensive package that fulfills your needs. This is of
course not always the case, so check with your (future) web host what options
you have.
Account upgrades
A second option is to upgrade to a more expensive web hosting package. Most
web hosting providers offer multiple hosting packages, from simple packages
for the beginner to advanced packages for demanding webmasters.
Believe it or not, very often it is the cheapest package that offers best
value for money. The difference between differently priced packages is very
often limited to disc space, data transfer and things like number of email
accounts and databases. Web hosting providers offering multiple domain hosting
in one account will normally allow more domains in more expensive packages.
Changing web hosting provider
Or maybe your current web host simply not has a package suited to your needs. This is not a curiosity because not all web hosting providers are trying to serve the whole webmaster community.
Some web hosting providers are specializing in
beginners, while other web hosting providers are serving the demanding end of
the market.
Changing web host should just be a matter of moving your files to
your new web host, and changing the name servers for your domain(s). In a few
hours or days, your website will be available at the new location with no
visible changes for your visitor. Note that different software and server
settings can require a little modification to your server side scripts.
Your previous web host have no possibilities
to sabotage your website if you did not register (or transfer) your domain(s)
with (to) them and you have backups of all your files. Even if your web
host is really angry with you, they can't do a thing to your website except
maybe cause a little downtime before you have set up your website and domain
with your new web host.