Halliday & Matthiessen (2014: 584):
… a mental process of desideration projects an exchange of the goods-&-services type, i.e. a proposal. If the Subject of the projection is the same as that of the mental process clause, the proposal is an offer, as in she wants to do it; if the two are different, then the proposal is a command, as in she wants you to do it. In the first type, the Subject is not repeated, but is carried over from the desiderative clause. (It can then be made explicit by a reflexive, as in she wants to do it herself.) All such projections could be treated as clause nexuses, as in Figure 8-13.