You are right that you can't have an error correction with just one bit of parity, you will need more than that.

What you have to take into account when using am error detection/correction code is the minimum hamming distance. This is the minimal number of bits that will be different between two valid codes.

Without any parity, the distance is 1, there is at least one bit that changes between two words. With a parity bit the distance becomes two, there will always be at least two bits that will be different between two valid codes. And other algorithms will have higher minimal hamming distance.

The minimal hamming distance will tell you how good the algorithm is to detect and correct errors. If the distance is high enough you can start correct bits, but for that you need to "sacrifice" some error detection.

With a minimal hamming distance of 3 for example, you may be able to detect up to 2 simultaneous errors, because any code with two bits flipped will not be a valid code. But if you have 3 simultaneous errors, then the new code will be detected as valid and none of the 3 errors will be detected.

Instead you could decide that you want to be able to correct one error. How the algorithm works in that case is that when an error is detected, it will "correct" the code by jumping to the nearest valid code. If you have only one error then this will work, it will always be corrected. But now if you have two errors, the algorithm will jump to the nearest valid code, by flipping only one bit, and the resulting code will be even worse than the original one, with 3 errors. You have created an algorithm that can correct one error, but for that you had to sacrifice double error detection.

Of course increasing the minimal hamming distance even further will enable you to detect or correct more errors. The general formula is h >= e + 2*c + 1 where h is the minimal hamming distance, e is the number of errors you want to detect, and c the number of errors you want to correct. The more you want to correct, the fewer you will be able to detect.