Yes that makes sense, and luckily there is a very convienient solution for that: the COUNT function.
You can find this under
Transform -> count values within cases.
Put all your questions in the "variables" box, and give it a name.
If you click "if", you can enter what should be counted (e.g., all variables with 1, 2, 3 or 4; all cases with system missing or whatever you like).
you can paste this into syntax to use it later too.