What's with this LevelThree business?
In the model expounded by ISO/IEC 9995, which is the international standard (set) that covers computer keyboards, keys can have one or more levels. What you may think of as "modifier keys" select amongst the available levels, sometimes in a complex fashion.
(Think of the operation of a mechanical typewriter, where the shift key actually moved part of the mechanism to a different level, and where the shift key often mechanically unlocked a "shift lock". Then mix in the ideas of other kinds of locks, such as ones that only apply to subsets of the keyboard such as the main block or the calculator pad.)
Sometimes the levels are what you see physically engraved upon the keys, sometimes (especially in the case of U.S. and European engravings and alphabetic keys) one or more of the levels are implied but not explicitly engraved.
Level 1 is unshifted; level 2 is the result of a ⇧ Shift modifier, a shift latch, a ⇫ Shift Lock, a Num Lock, or a ⇬ Caps Lock; and level 3 is the result of a "level three modifier" of some kind.
As you can see from this configuration file, a "level 4" convention exists (an extension to ISO/IEC 9995 proper) that is the result of applying both level 2 and level 3 shifts at the same time.
(This convention presupposes that this combination is even available in the first place. In some keyboard layouts, there is no ⇨ Group 2 key, and the keys that would otherwise select "level 4" instead select the second group, which is an entire alternative layout complete with its own set of 3 shift levels. On actual keytops, group 2 is a second column of one to three engraved symbols on the right. A lot of complexity in some systems results from trying to pretend that group 2 does not exist, whereas level 4 does.)
A level three modifier is generally the ⇮ AltGr key, to the right of the spacebar. On some keyboards the key that generates the relevant HID code, down the wire from the keyboard to the main unit, is labelled ⌥ Option and its physical position (still on the right) is slightly different. Software sees it as the same key, whichever the engraving and physical position. Do not, by the way, confuse it with the similar key that is to the left of the spacebar. That is a different key.
Not all software keyboard layouts make this key into a level modifier, however. What keys are modifier keys is (with one exception) entirely determined by the software keyboard layout. In some software keyboard layouts the key in that position is treated as another ⎇ Alt. If this is the case, one has no way to type a level 3 shift, absent using another keyboard layout or patching one's current keyboard layout so that some key or combination of keys produces a level 3 shift.
In a SI 1452 layout, ⇮ AltGr is indeed the level 3 shift, and with it you should be able to type all of the Niqqud. I suspect that you have conflated ⎇ Alt and ⇮ AltGr.