Block ciphers are already built of multiple components:
AES = fixed 8-bit sbox, MDS matrix multiplication, 8-bit rotations
Twofish = key dependent sboxes, MDS matrix, 1 and 8-bit rotations, PHT
Chaining ciphers adds more components, more rounds, more complexity
Depending on chaining implementation, a different IV is not required for each cipher.
For example, the first algorithm uses the selected mode, and the next in the chain only use ECB; or the other way around. Choosing the modes and the order they are chained is important.
Different keys should be used, otherwise there is no increase in effective key space, just cipher complexity and round count.
As long as the algorithms are not some kind of inversion of eachother, it effectively increases the total keyspace of the cipher chain, in addition to increasing the round count. Additionally, the different building blocks make certain attacks more difficult, where the similarity between rounds is exploited. It is better to build a cipher with more complexity than rely on the complexity of the chain, as one complete weak cipher may be "peeled off".
Rounds of one cipher cancelling out rounds of another is a distinct concern, and if the ciphers are the same (DES to 2DES, 3DES,.. NDES) there are attacks that will exploit this and reduce the effective key space. Assuming the underlying block ciphers are strong against all attacks, the upper bound on the chain security will be the combined upper bounds of each cipher's security, but can be lower in practice, especially if implemented poorly.
I tried to summarize points in one of the comments to the original post, certain points may be unclear or not touched upon