It seems this would only be a risk if the very last hashing function were compromised. Even then you would need to know how to generate the correct input to the last hashing function using the other hashing functions. It seems inherently more secure to me.
Sadly, no. To understand this, consider the collision problem inherent to all hashing functions.
if hash1(x) has collisions, then so does hash2(hash1(x)) and hash4(hash3(... and so on, until we reach the full hashing stack, which also has collisions. Similarly, if hash2, hash3, etc, or hash11 have collisions, then so does X11(x). Simply put, if there's a collision attack for any hash#(x), then the same attack applies to X11(x).
A much better way to implement multiple hashing functions would be to interleave multiple hashes, not chain them.
Basically, X11 is 11 times more vulnerable to collisions then a single algorithm would be, while offering no real-world benefits at all.