With more attributes the problem rapidly becomes more difficult.  People can think clearly about two attributes at a time; the simultaneous consideration of three or more is difficult.  The number of pairs of attributes to consider grows quadratically with the number of attributes: 10 pairs for 5 attributes, 45 pairs for 10 attributes, 105 pairs for 15 attributes, 190 pairs for 20 attributes, and so on.
Fortunately, the theory provides some powerful methods to establish whether shortcuts are possible.
It boils down to this: if you can establish, say, that trade-offs among three attributes do not depend on the values of the other 17 attributes, then you do not need to consider individual trade-offs between the 3 * 17 pairs of attributes involved.  Instead, you can develop an overall score for the 3 attributes and (perhaps) another score for the remaining 17.  Then you need to consider trade-offs between these two scores.  This can be explored using specific examples.