IMHO the main essence of a Feistel cipher of block length $n$ is the working of a non-linear function $F$ that is applied to the two halves of the block of length $n/2$.
Now suppose a certain block cipher of block length $n$ as well as two keys of it are given. If one employs the given block cipher in the sense of $F$ on each half of a larger block of length $2n$ in parallel (actually invoked alternatingly with the two keys) for a number of rounds, one obtains evidently a new block cipher of Feistel genre having doubled block length and requiring a doubled key length.
Could anything in general be said on the security (or insecurity) of such a scheme?
It may be of interest to also examine the special case where the two keys are identical.
The scheme can be trivially generalized to achieve a block length of the larger cipher of $m \times n$ where $m \geq 2$ operating on $m$ subblocks of length $n$ as follows, with $E(K,P)$ denoting the given block cipher and $K[*]$ denoting the array of the keys:
for i in [1 .. number_of_rounds] do for j in [1 .. m] do subblock[j+1 mod m] ^= E(K[j],subblock[j])
Note that, in case $m$ is not fixed but the plaintext length is $m \times n$ (and there is one or more keys) one obtains a special kind of block chaining with the given block cipher.
Certainly there is an efficiency issue that needs to be examined for practical applications of the scheme.