[Sharkû]

"Of this Order the number is unknown; but of those that came to the North of Middle-earth, where there was most hope [...], the chiefs was five." (UT, IV, ii)

Unfortunately, an ambiguous remark, for it could both refer to the Heren Istarion, and the Order of the Ainur:

" Wizard is a translation of Quenya istar (Sindarin ithron): one of the members of an "order" (as they call it), claiming to possess, and exhibiting, eminent knowledge of the history and nature the World."
But also: "they belonged solely to the Third Age and then departed". (ibid.)

This could imply that the Heren Istarion was an ad hoc formation of the five Maiar that were to go to Middle-Earth as messengers.

On the other hand, two quotes make it likely that the Order of unknown number is the order of the Ainur:
"Emissaries they were from Lords of the West, the Valar, who still took counsel for the governance of Middle-earth, and when the shadow of Sauron began first to stir again took this means of resisting him. For with the consent of Eru they sent members of their own high order..." (ibid.)
This 'members of their [the Valar's] high order' precedes the 'of this Order the number is unkown', it is therefore likely the latter refers to the Valar.

Note also that in the Istari essay at hand, the term Istari always only means the five that went to Middle-Earth and are known to us, I consider it unlikely that a line such as "Indeed, of all the Istari, one only remained faithful" (ibid.) could leave the possibility of Istari in Aman at all, being that they would not fall like those that went East.

"We must assume that they [the Istari] were all Maiar, that is persons of the "angelic" order, though not necessarily of the same rank. [...] Saruman is said (e.g. by Gandalf himself) to have been the chief of the Istari – that is, higher in Valinórean stature than the others. [...] It may be seen that they were free each to do what they could in this mission; that they were not commanded or supposed to act together as a small central body of power and wisdom;" (ibid.)

Again, we have the order of the Ainur, and no hint of a order of the Wizards beyond the five. The leading rôle of Curunír is, as the quote shows, only due to the 'Valinorean' stature, not stature in the Heren Istarion -- the first led to the latter, obviously, implying that the HI was indeed an ad hoc formation.
Also note that the last line given above shows that there hardly was such a thing as an 'order' even in Middle-Earth; had there been a fixed unity between the five aforehand, it can assumed to have been otherwise.

The council of the Valar -- "a council of the Valar, summoned it seems by Manwë ("and maybe he called upon Eru for counsel?"), at which it was resolved to send out three emissaries to Middle-earth" is also of utmost importance for the question.
Not only does it show that the Valar did not consider the Heren Istarion as the body from which to recruit the messengers, it is also highly interesting that the number originall designed by the Valar to depart East was three, and the other two only joined for other, practically unnecessary reasons, hence making the image of the 'hand' even less likely (though not less striking).

In short, the conclusions that can safely be drawn from an attentive reading of the Istari essays would be that the order of the Heren Istarion consisted of the five Wizards we know, and that it only came into being with their mission, and ceased to exist with the passing of Saruman at the latest. There were obviously no Istari in this narrow sense beyond the five.
Linguistically, of course, istari, wizards, means nothing more than 'versed and wise in the ways of the world' (see above). Now, undeniably, this can be applied to all Ainur, and the question about the number boils down to a question about the definition of the term Istari. If we are to distinguish the Five from the other Ainur for their mission they went on, we are led to the differentiation explained above (it is clear that throughout most writings, and practically all analysis thereof, this distinction is made).
If the Five are seen as Istari together with all other Ainur, no less wise than they, one obviously comes to the same conclusion -- for the number of the Order of the Ainur is and will remain unknown.