Very low confidence, because you have given so little context. For example this could well be a company that is not a member of a Group of companies: "company outside the Group"/"non Group company". The answer given would fit a contract where the "terza società" is not one of the two parties to the contract.

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Note added at 11 mins (2011-10-07 09:06:37 GMT)
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By the way, the rules for closing questions:

2.6 Askers must close "help" questions. Close questions by selecting the answer deemed **most helpful** (and awarding it points, unless the question was posed as "not-for-points").

http://www.proz.com/?sp=siterules&mode=show&category=kudoz_a...

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Note added at 43 mins (2011-10-07 09:38:45 GMT)
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I think you need to understand precisely what is meant by “terza società” in your context (give some more of it).
The word “terzo/a” is used much more frequently in Italian than “third party” is in English. For example the “terzi” in the financial statements of a construction company are usually the “contractors”, or when a company sells its VAT credits to a “società terza” this is really just another company, where the first party is the company, the second is the tax authorities and the third party is just another company. “terza” is often used for “independent”.
If there is a Group that is central to the picture then “outside the Group” or “external company” is probably what you need, but from “third party company” to “non Group company” might be too long a step to ask your reader to make.