Martin (1992: 314-5):
Next, extension. With extension distinct meanings are combined. The contrast between Process°Range:process and Process°Medium structures in the clause, and Classifier°Thing and Epithet°Thing structures in the nominal group has already served to illustrate the difference between elaboration and extension at issue here. Where Range:processes elaborate a Process, Range:entities (Halliday 1985: 134-5) and Mediums (Halliday 1985: 144-5) extend them as outlined in Table 5.11.
Table 5.11. Extension in the clause Clauseprocess + range:entity process + medium climb mountain shoot terrorist play piano hug friend cross court cook rice like tennis please crowd (it pleased them that…) see play strike me (it struck me that…) consider text convince audience (it convinced them…)
 Extension, like elaboration, enhancement and projection, is a logico-semantic relation. It includes the relations of composition (meronymy), possession and association.
 As previously demonstrated (here and here), it is not the case that 'the contrast between Process°Range:process and Process°Medium structures in the clause, and Classifier°Thing and Epithet°Thing structures in the nominal group has already served to illustrate the difference between elaboration and extension at issue here'. (Process and Medium are not related by extension; in the examples provided, both Classifier and Epithet elaborate the Thing.)
 Neither Range:entities nor Mediums extend a Process. On the one hand, in SFL, expansion and projection relations obtain between the Nucleus (Process/Medium) and the rest. On the other hand, the relation between the Nucleus and Range:entity depends on the process type. In material processes, the relation is enhancement, not extension. In mental and verbal processes, the relation is projection, not extension. See Halliday & Matthiessen (1999: 175).
Thus, none of the six examples involve extension. In the first three, the relation is enhancement, not extension, whereas in the last three, it is projection, not extension.
 'Tennis' and 'play' are processes, not entities. Martin (1992: 311):
As Halliday (1985: 135) points out, "Tennis is clearly not an entity; there is no such thing as tennis other than the act of playing it."