In Down syndrome only one chromosome is duplicated (so there are three instead of the normal two) as is the case with a few other syndromes caused by an extra copy of a single chromosome. Usually you only see physical characteristics if it is a sex chromosome (X or Y) because there will be a overdose of one or the other hormones.

If all of the chromosomes are doubled or tripled then there will still be the correct ratio of proteins, enzymes or hormones just maybe more. Polyploidy is very common naturally in plants. One of the reasons that plants can do fine with an extra set of chromosomes is because with the doubling or tripling the cell has to be larger. That won't bother a plant but could cause major deformities in an animal.