DES 48-bit round keys replaced with 48-bit block keys
Let the DES-variant's key $k=sk_0|sk_1|...|sk_{15}$, where each $sk_i$ denotes a 48-bit subkey and "|" concatenation. Due to the Feistel nature of DES, a sufficient condition for $sk_i$ is that for $i \in [0,15]$, subkeys $sk_i = sk_{15-i}$. They will work as each others' complements and encryption will become identical to decryption. There will be $2^{48*8}=2^{384}$ such sets, or keys $k$. Relatively speaking this is still far less than the number of weak keys in original DES, due to the large number of freely selected key bits.
The semi-weak key definition makes sense only in the original DES, where the round keys depend on the secret key: both the definition of weak and semi-weak keys aim at producing identical round keys for encryption and decryption; the weak keys are sufficient to accomplish this by themselves, as semi-weak keys come in sets. 


P.S. I have hard time imagining any other purpose for this kind of cryptosystem than purely educational