The answer is simple "make the code space bigger". This is exactly what has been done and what is being done at the moment.
The CJK (Chinese, Japanese, Korean) character sets needed a lot of space so they invented 16-bit codes for their character encoding. Unfortunately although the Chinese ideograms are part of all forms of Chinese and Japanese and Korean they invented at least four different encodings. This meant that transfer of text could only be done via massive look-up tables to convert the character encodings from "foreign" to local before the local system should display the message.
The need was obvious and pressing for a unified encoding standard. And the technology was available to support it.