knot

I don't think if it is a language question.
Anyway,
Can "a willow tree" have more than one knot, not the burr knot but the standard knot?

This definition for knot from our dictionary may be helpful:

the hard, cross-grained mass of wood at the place where a branch joins a tree trunk;
a part of this mass showing in a piece of lumber.

Willow trees have many branches, so willow trees can have more than one knot.

To expand on Owlman's reply, it is lumber (wood) that normally has knots in US-English, not living trees. I think we need some context and perhaps a sentence to figure out what it is that you are asking.

LVRBC said:

it is lumber (wood) that normally has knots in US-English, not living trees.

The same in BE, but we call lumber timber.

I learned a lot about this knotty subject here: Why Does Wood Have Knots? » Science ABC
It seems that living trees do indeed have growths called "knots."

LVRBC said:

To expand on Owlman's reply, it is lumber (wood) that normally has knots in US-English, not living trees. I think we need some context and perhaps a sentence to figure out what it is that you are asking.

Living trees have knots and boards both have knots. Knots don't suddenly appear when wood is sawn into boards. They're just harder to see in a living tree, where they look like knobs or lumps in the bark. An old pine tree can have lots of knots (and produce 'knotty pine' boards) boards, because pine trees tend to produce a lot of branches relatively low on the trunk that die off as the tree grows higher. Knots form at the base of the dead branches.
In the US (see #4) timber is commercially-useful wood in its living state. The process of cutting it down is 'timber harvesting.' Once it is turned into boards, it's lumber.

Yes, of course the knots form in the living tree. However, it unusual to speak of knots in willow trees, so I still feel we need context to know what the OP intends. It is language, not botany, that is under discussion here.