You can't actually form a std::string without copying the data. A stringstream would probably reuse the memory from pass to pass (though I think the standard is silent on whether it actually has to), but it still wouldn't avoid the copying.
A common approach to this sort of problem is to write the code which processes the data in step 3 to use a begin/end iterator pair; then it can easily process either a std::string, a vector of chars, a pair of raw pointers, etc. Unlike passing it a container type like std::string, it would no longer know or care how the memory was allocated, since it would still belong to the caller. Carrying this idea to its logical conclusion is boost::range, which adds all the overloaded constructors to still let the caller just pass a string/vector/list/any sort of container with .begin() and .end(), or separate iterators.
Having written your processing code to work on an arbitrary iterator range, you could then even write a custom iterator (not as hard as it sounds, basically just an object with some standard typedefs, and operator ++/*/=/==/!= overloaded to get a forward-only iterator) that takes care of advancing to the next fragment each time it hit the end of the one it's working on, skipping over whitespace (I assume that's what you meant by trim). That you never had to assemble the whole string contiguously at all. Whether or not this would be a win depends on how many fragments/how large of fragments you have. This is essentially what the SGI rope mentioned by Martin York is: a string where append forms a linked list of fragments instead of a contiguous buffer, which is thus suitable for much longer values.
UPDATE (since I still see occasional upvotes on this answer):
C++17 introduces another choice: std::string_view, which replaced std::string in many function signatures, is a non-owning reference to a character data. It is implicitly convertible from std::string, but can also be explicitly constructed from contiguous data owned somewhere else, avoiding the unnecessary copying std::string imposes.
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