Is it possible to find additional key pairs resulting in the same address that I already control?
It's not possible, practically speaking.
A P2PKH Bitcoin address is computed as RIPEMD160(SHA256(publickey)). Since public keys are unique, to find another keypair that results in the same address, you're essentially trying to find a hash collision on SHA256 or RIPEMD160, which is extremely difficult.
The most &quot;efficient&quot; way to find such a collision would be to iterate over the entire private key space.