Well Larry, DEMÁS= is used to mention or include other people or thing. Yo voy al cine con las DEMÁS personas de mi clase. Yo terminaré lo DEMÁS luego. DE MÁS= is to mention an extra. Yo tengo 10 dólares DE MÁS.

además: It is an adjective that can sustantivarse as indefinite pronoun meaning 'the other, the other, the other or the other, the other'. After the mention of a number of elements, appoints the remaining belonging to the same group as mentioned above, or the missing part of a whole. As an adjective, it is preceded by an article or possessive prefix to plural nouns or collective de más: It is an adverbial phrase meaning 'to spare too much': "What you are most in life is envy, hatred, resentment ..." If the neutral article preceded it, it is opposed to the least and means 'the most important': "The most important is to trust our friends." "... Trust in God and in Senor Don Quixote, that you must give a kingdom, not an island. So much the more as less said Sancho -; ... "(Cervantes, Don Quixote). Also part of the buildings speak more ('say inconveniences') and being more ('spare room' or 'clutter'): "He kept compromising documents for use against your partner if he spoke more" "Perhaps in every marriage comes the day when the conversation is over and upset a pain in the mouth." (Augusto Casola, "The Sunken Cathedral")