By the associative property of multiplication, it doesn't help to insert parentheses that specify the order of multiplication. For example, the associative property tells us that $ (2\cdot(3\cdot 4))\cdot (5+1) $ is the same as $ 2\cdot3\cdot4\cdot (5+1) $. So the only way to get different values is to group +1 with a different number of factors. We get \begin{align*} 2\cdot 3 \cdot 4 \cdot (5 + 1) &= 144, \\ 2\cdot 3 \cdot (4 \cdot 5 + 1) &= 126,\\ 2\cdot (3 \cdot 4 \cdot 5 + 1) &= 122, \\ (2\cdot 3 \cdot 4 \cdot 5) + 1 \hphantom{)} &= 121.\end{align*} In total there are $ \boxed{4} $ possible values for the expression.