Firstly, let us look at the term itself. Abra-Melin uses various terms interchangeably: "Holy Guardian Angel", "Guardian Angel", "Holy Angel", or, in some cases, just "Angel", all referring to the same thing. This is usually referred to today by most as simply "Holy Guardian Angel". However, in his Introduction, Mathers only ever uses the term "Guardian Angel".
Neither the term “Holy Guardian Angel” nor "Guardian Angel" is overtly used, to my knowledge, in any original G.D. material. There is a Stella Matutina reference highlighted by Alex Sumner in relation to the 6=5, but the S.M. diverged on a number of things, not least of all the approach to Adeptus Major (compare with, for example, the original 6=5 Ritual in my book The Complete Initiation Rituals of the Golden Dawn).
Crowley, while not always a reliable witness, did give an interesting comment in relation to the varying names for the Holy Guardian Angel in different systems in The Equinox:
“The Golden Dawn calls him the Genius.”
The G.D. did indeed speak of an Angel, and this was equated with the Higher Genius, which has been very much misunderstood. G.D. material teaches that we have an Angelic Form, an Archangelic Form, and a Divine Form. See this line from Ritual V:
“This Great Angel is the Higher Genius, beyond which are the Archangels and the Divine.”
While this can be likened to the Holy Guardian Angel, it is better to see this as part of the Human in its totality (where the Human comprises four planes, the lowest being the Human Form we are all used to). In this sense, then, the G.D. teaching is more expansive.
Remember the goal laid out in the Obligation taken by a 5=6:
“I further solemnly promise and swear that with the Divine Permission I will from this day forward apply myself to the Great Work, which is so to purify and exalt my spiritual nature that with the Divine Aid, I may at length attain to be more than human, and thus gradually raise and unite myself to my higher and Divine Genius, and that in this event I will not abuse the great power entrusted unto me.”
Let us compare this with the goal outlined by Mathers in his Introduction to Abra-Melin:
“From this it results that the magnum opus [great work] propounded in this work is: by purity and self-denial to obtain the knowledge of and conversation with one's Guardian Angel, so that thereby and thereafter we may obtain the right of using the Evil Spirits for our servants in all material matters.”
Clearly there are key differences here, not least of all the latter's focus on the use of Evil Spirits. Both, however, are presented as a Great Work, and this Great Work has a primary focus on an Angel directly related to the individual, referred to in Abra-Melin as a Guardian Angel, and referred to in the G.D. system as the “Higher Genius” (which, as we have seen before, is a Great Angel). The process of connection differs, however, in that the former focuses on “knowledge of and conversation with” the Angel, while the latter focuses on uniting with that Angel (and also, as we shall see, the Forms beyond).
Could Mathers have intended these to be the same, as Crowley suggests? That is certainly possible, though the fact that he chose not to use the same terminology suggests he saw this in a different manner, as we see by the different methodology and goal, and the addition of a connection to and ultimate union with Higher Forms. I am more inclined to believe that the Holy Guardian Angel from Abra-Melin was an inspiration for Mathers, rather than a concept he would employ wholesale.
Indeed, the term “Guardian Angel” may suggest too limited a notion, whereas the Roman concept of the “Genius” has a much wider applicability. Both share the idea of a protecting spirit assigned from birth, but the Roman view expands to include all beings, and even locations and entire nations (which is supported by Mathers' references to the Genii of nations in G.D. material). In this sense, then, the Higher Genius is but one Angel from a vast Choir.
The aim, therefore, is to “gradually raise and unite [oneself] with [one's] higher and Divine Genius”. Some see this as the same, singular Genius, but I see these as different—i.e. the Higher (Angelic) Genius, which is most within reach, but also the Archangelic Genius and then the Divine Genius beyond.
All of this is achieved "at length" and "gradually", suggesting this is not a goal one can expect to achieve via a single ritual or operation. Certainly, I am skeptical of any who claim to have completed this Great Work.
One may also begin to understand, then, what is meant by "to be more than human". It is to be Angelic, Archangelic, and Divine.
There is an article on this topic by Frater A.R.O. in Vol. 6 of The Light Extended. [Available here.]