Besides the main moves 2.d4 and 2.Nf3 one encounters (much more rarely) the bishop moves 2.Bb5 and 2.Bc4 and the knight move 2.Nc3.
1.e4 Nc6 2.Bb5
The rarely played bishop move to b5 is not as crazy as it first looks: a figure is developed, the question of the formation of the pawn centre e4d4 remains unanswered for the time being, and there is a “threat” of hitting c6 with the creation of a double pawn. The latter is of course only a threat to a limited extent, because White has to give up the bishop pair for this – which is of more far-reaching importance in grandmaster chess than in amateur chess (let’s stay honest).
The intention of White becomes clear when looking at the official name of this opening variation: Pseudo Spanish variation of the Nimzowitsch Defence. White wants to transfer into Ruy Lopez if at all possible and thus degrade the TDKS to a mere transposition of moves. Black should neither do him this favour, nor let himself be provoked into knight moves by the threat of a exchange on c6. The easiest and best is 2… d5.
1.e4 Nc6 2.Bc4
The likewise less frequently played bishop move to c4 hopes for a transformation into Italian (e.g. after 2.Bc4 e5 3.Nf3), but sharp constellations quickly emerge. Black can attack the pawn e4 with 2… Nf6 because of the pawn fork d7-d5, and either White gives up his pair of bishops (by striking at f7) or he “normally” swaps to e4, but then the position weakens and after a few moves there is nothing noticeable left of the white advantage.
1.e4 Nc6 2.Nc3
This rarely played knight move is by no means a mere “symmetrical move”. Similar to all other second moves except 2.d4, Weiß aims at a transposition of moves and a transfer into open systems, here specifically into the Vienna Game, which is created in the classical way after 1.e4 e5 2.Nc3. The mere fact that the classical Vienna Game is far less popular than, say, Ruy Lopez or Italian saves the TDKS player this continuation in practice – for it is not at all easy to avoid the transition to a classical opening here.
Perhaps 1.e4 Nc6 2.Nc3 is the only move sequence in which Black is better advised to accept the offer to move to a classical opening (here the Vienna Game) with 2… e5. As is well known, he does not have to fear much in the Vienna Game.