The two chord is a minor chord, but again, let us use the more ambiguous minor 7th chord. This is played using this shape, 2 frets up from the one chord. Notice it is a different shape to the previous minor 7th chord. This is because the root is on a different string. No need to worry about why this is - just learn that the two chord is this shape at this location!
Notice that the notes on strings 3,4 & 5 are common with our previous four chord. practically, this means you can substitute one for the other. I like to think of it as another way to play a four chord since the four chord is do often a main chord in songs. However, depending on the song you have chosed one might sound better than the other - your ear will tell you which one!
Alternatively, the normal minor chord can be played by adding your little finger (4) like this: