Can we do Multi-Prime Diffie-Hellman? What is the correct way, if any, to do Multi-Prime DH?
From security point of view, is there any benefit to do it?
Multi-Prime is not about multi participants.
Multi prime is when we use two or more prime numbers and multiply them to get the modulus part in DH.
It is faster to find four 4096 bit safe primes and multiply them than to find single 16384 bit safe prime.
The question is if a multi-prime will yield valid and secure key exchange procedure.
And if so, what will be the procedure to get good g and p.
By Multi-Prime DH, I assume you mean something analogous to Multi-Prime RSA.
In Multi-Prime RSA, we pick a modulus with three (or more) prime factors; because the holder of the private key knows the factorization, he can compute (using the CRT optimization) using smaller prime modulii (and smaller exponents), yielding a moderate speed-up.
Given that is what Multi-Prime RSA, what would Multi-Prime DH be?  I assume that it is one where we pick a modulus with two (or more) prime factors.  If we know the prime factors, then we can use the CRT optimization (similar to how it works in RSA) to get a two time speed up in the DH operations (assuming two prime factors).
So, if that's the benefit, what's the downside?  Will if the attacker learns the factorization, he can use it to attack each prime factor of the modulus individually; this would yield a significant improvement in this expected effort.
So, what do we conclude?  Well, this would be a moderate optimization (factor of 2) for one side (we can't assume both sides know the factorization), at the risk that the adversary learns it (in which case it drastically reduces the security level).
Hence, I cannot recommend it.

Update: on reconsideration, I do see one scenario where it might make some sense; if you are generating ephemeral Diffie Hellman groups (which is quite unusual, however I have run into knowledgable people who have advocated for it); in that case, searching for (say) two 2048 bit primes is much simpler than searching for a single 4096 bit primes.  In addition, in that case, we wouldn't have to worry about whether $p-1$ has small factors (because the corresponding value for $\phi(n)$, which the adversary wouldn't know).  The security of the system would rely on the difficulty of factoring $n$ (as that factorization process would dominate the time taken by the discrete log problem modulo the smaller primes).  Hence, in this corner case, it would make some sense.