I'm assuming you did not know the name of its author.
When you post problems that aren't your own, you owe it to the composers to acknowledge their work. This is a problem by J. C. J. Wainwright, and is in two moves. (It was first published in Alain C. White's Theory of Pawn Promotion, 1912.)
And, no, it has only one solution. (Added explanation: In the problem world, a 'solution' is the first move (the key move), and all subsequent variations that meet the limits of the stipulation, which in this case is 'self-mate in two moves'. Problems that have solutions with more than one key move are considered to be faulty, unless there are good reasons for the number of key moves.)
If you want to double check, try the on-line chess problem database YACPDB (https://www.yacpdb.org/), where a lot of chess problems have been recorded by users. Here is the link directly to it: https://www.yacpdb.org/#262458