Is there way to combine secrets first and later split them?
On the information theoretic level you can not get a shorter result than the concatenation if you want to be able to recover the original inputs: If there are $k$ shares from a set with $2^{x}$ elements (represented as $x$ bit array), an injective function requires at least $(2^{x})^k = 2^{xk}$ different function values, which requires at least $xk$ bit. If the function combining the different shares has a shorter function value, it is not injective and you can not recover the original shares.

However, since the chosen string has a specific bit representation, you might be able to work with encodings to save space, e.g. Huffman codes, etc.

You might be able to choose your common secret and shares in a way, where the shares are not compressible by much but the common secret is.