Sure, you may have two keys generate the similar handle.
There are 2^160 doable addresses, and a couple of^256 doable personal keys, so every handle corresponds to roughly 2^(256-160)=2^96 personal keys. Any of those will generate the identical handle and thus be capable of spend the cash owned by that handle. Since 2^160 is so giant, nevertheless, it might take a near-eternity to seek out any collisions.
Whether or not two personal keys can generate the similar public key is one other query. I feel the reply is sure, however I’m not certain on that. The general public key in uncompressed kind consists of two 256-bit numbers, that are X and Y coordinates on an elliptic curve. Nevertheless, the compressed kind is simply the X coordinate plus a bit, from which you’ll be able to calculate the entire public key. This implies the house is (at most) 2^257. Until there’s a one-to-one mapping as a result of mathematical properties of the cryptography used, every compressed public key corresponds to roughly 0.5 personal keys (with the identical distribution you’d get from selecting a random quantity from 1 to 2^257, 2^256 occasions), so some personal keys will collide, whereas others is not going to.
Truly discovering any pair of various personal keys that generate the identical public key or handle can be fairly tough. Both it might contain an enormous quantity of computation and/or luck, or it might be resulting from discovering a critical vulnerability within the algorithm(s) used.