Mīmāṃsā authors took a different way and stated that the self is not changeless. Not in the abvoe way, at least.
A great contemporary Mīmāṃsā scholar, K.T. Pandurangi, writes:
"The concept of substance of the Bhāṭṭas and the Prābhākaras is the same as that of the Nyāya-vaiśeṣikas. However, in the case of ātman, which is considered as a substance, the Bhāṭṭas accept pariṇāma or avasthāntara in the process of cognition" (Pandurangi 2006, p. 104). "[T]here is am important difference between the Bhāṭṭa concept of ātman and the Nyāya-vaiśeṣikas concept of it. While cognition is an attribute of ātman according to Nyāya-vaiśeṣikas, it is a modification or a state of ātman according to Bhāṭṭas'' (Pandurangi 2006, p. 145).
Pandurangi's Pūrvamīmāṃsā from an interdisciplinary point of view is an excellent book. Unfortunately, very much like Indian classical works, it rarely mentions the exact source of a certain statement. In this case, it is probably Kumārila's Ślokavārttika, Ātmavāda:
(nānityaśabdavācyatvam ātmano vinivāryate | vikriyāmātravācitve na hy ucchedo 'sya tāvatā || syātām atyantanāśe 'sya kṛtanāśākṛtāgamau | na tv avasthāntaraprāptau loke bālayuvādivat || 22cd-23cd)It is not prohibited to say that the self is not fix (nitya) |
if what one means is just that it can evolve (vikriyā), [since] there is no cessation of it by that ||
If there were an absolute destruction of it, there would be destruction of the actions performed and accrual of actions non-performed |
but not in the case it reaches a different stage, like in the ordinary experience of childhood, youth and [adulthood] (when the same person is said to be a child, then a young person and then an adult) ||
On the subject in Mīmāṃsā, see this post (on Prābhākara Mīmāṃsā views) and the tag "subject".