Based only on the core rulebook (there could be something contradicting this answer in other books), I'd say it is practically impossible to "uplift" a muse. Here are a few reasons.
AI is fundamentally different from AGI
Most AGIs emulate human brain in software, which is why they can be sleeved in a biomorph. This is (I suspect) mostly done not because there's a particular benefit to biobrains, but in an effort to make AGIs more "human". AI, however, is not intended to relate to humanity, so it is not designed to operate in such a fashion. They learn, but they don't improve. While still likely a neural net rather than an "if-then-else" procedural code written by humans, AIs would probably operate in a different fashion than AGIs. Uplifts, by comparison, are based on regular animals whose brains are biological and operate similarly to those of humans.
Adult animals don't get uplifted
You can't take your favourite pet and uplift it. Rather, this requires fundamental genetic manipulation that changes the nature of the species in order to allow it to develop sentience. Uplifts are born uplifted.
AGIs are brought up, not made
Relating to the previous points, AGIs go through their own process of growing up, gradually developing their capabilities and personality. It is not a question of giving an AI more processing power and removing artificial restrictions placed on it.
With all this in mind, making an AGI version of a muse would likely require creating some sort of personality template based on it, to be used as a seed for a new AGI to be grown out of. Which means the result would not be a "real boy" version of your muse, but a new person that may sometimes remind you of your muse. This process would also take years, even in accelerated time.
Which means your best bet would probably be to carry the developing AGI with you in a ghostrider module, while still using the AI muse as a personal aide. In effect, you'd have its uplifted child with you, that may, eventually, grow up to replace it. If it's willing.