Halliday & Matthiessen (2014: 639):
Since the verbal group consists of Finite plus Predicator, it follows automatically that any clausal ellipsis in which the Mood element is present but the Residue omitted will involve ellipsis within the verbal group: the Predicator will be ellipsed together with the rest of the Residue, as in Have a shower! – I can’t [∅: have a shower]. There is no need to repeat the discussion of this phenomenon. The ellipsis may affect only part of the Predicator, as when the Predicator is realised by a verbal group complex and only the first part of the complex is retained together with the infinitive marker to:Have you do you read very much Kafka? I am trying to [∅: read very much Kafka], yes, ... [Text 125]
“Can you hop on your hind legs?” asked the furry rabbit. – “I don’t want to [∅: hop on my hind legs],” said the little Rabbit. [Text 28]
Here the rest of the verbal group serving as Predicator is ellipsed together with the remainder of the Residue.