How many Istari came to Middle-earth?

[The Saucepan Man]

Now, before eveyone yells "five, of course!" and directs me to the numerous other Istari threads (which I have skimmed through), hear me out. I have just read the chapter on the Istari in Unfinished Tales and came across the following:

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 were five.

The first part of this sentence is referring to the Order of Wizards, the Heren Istarion. I assume that their number is unknown because not all of them came to Middle-earth. But the second part of the sentence suggests to me that more than the five that are named may have come to Middle-earth.

First, the sentence is referring only to those who came to the North of Middle-earth, suggesting that there may have been others who were sent to the South. Of course, it may equally be that none were sent to the South and the reference to "the North" is included merely to make the point that this was where there was the most hope and therefore where those that were sent could have the greatest effect.

But it is also said that the chiefs of those sent to Northern Middle-earth numbered five. Might this suggest that more than five were sent but that those who are named were the greatest, ie their chiefs? Otherwise, why not simply say that "Of those that came to the North of Middle-earth, the number was five" or something similar?

Now, I realise that other references in the chapter suggest that there were only five. For example, the paragraph from which the quote given above comes names five Istari, with Mithrandir (Gandalf) being described as the last arrival. But this does not preclude there being other un-named Istari amongst those who came. It just means that, of all those who came (the chiefs of whom are named), Gandalf came last.

Later in the chapter, it is said that:

The two highest of this order (of whom it is said there were five) were called ... Curunir ... and Mithrandir ...

But this only refers to it being said that there were five. It is therefore not conclusive. And it is also in reference to the "order", of which the quote given earlier says the number is unknown.

So could it be that more than five Istari travelled to Middle-earth, or are there further, more conclusive, references that establish the number as five? And, if so, why are the named Istari referred to as the chiefs of those who came?