I would like to know if once in the Schengen area it is possible to extend a tourist visa for more time?
Generally no. Exceptions are allowed only in emergency.
For example, The Netherlands state
Can I extend a Schengen visa in the Netherlands?
You can only extend a short-stay Schengen visa in emergencies, for example if you become ill. Strict conditions apply.
Conditions for extending a short-stay Schengen visa
To be allowed to extend your visa, you must meet the following conditions:
- Your stay in the Schengen Area must not exceed 90 days in total. If you stay longer than 90 days, your visa will be limited to the Netherlands.
- You must explain why you need to extend your stay. If you are unable to return to your own country before your visa expires, you will need to show documents to demonstrate why.
- You must have enough money for your stay in the Netherlands (at least €34 a day). Or you can ask someone to act as a guarantor.
- You must have valid travel and/or health insurance.
- Your passport must be valid for at least another 6 months and must not be more than 10 years old.
- There must be no indications that you have other reasons for extending your visa, for example illegal residence in the Netherlands.
- You must pay a fee to extend a Schengen visa.
An Italian Website also says that there must be "reasons of force majeure, humanitarian reasons or serious personal reasons" not just because there are some places or people you'd like more time to see.
I expect the rules are the same (or very similar) across the EU.
It's hard to say without knowing which passport you hold. And I'm certainly no expert on European visa's. But just a quick check on wikitravel I found http://wikitravel.org/en/Travel_in_the_Schengen_Zone. I hope that helps.