You can take full control of the buffer used by writing the buffer yourself and using that buffer in the stringstream
stringstream membuf(std::ios::in | std::ios::out | std::ios::binary);
membuf.rdbuf(yourVeryOwnStreamBuf);
Your own buffer should be derived from basic_streambuf, and override the sync() and overflow() methods appropriately.
For your internal representation you could probably use something like vector< char >, and reserve() it to the needed size so that no reallocations and copies are done.
This implies you know an upper bound for the space needed in advance. But if you don’t know the size in advance, and need a continguous buffer in the end, copies are of course unavoidable.