You can throw a whole necklace for the equivalent of an "11th-level" Fireball
The description of the Necklace of Fireballs reads (DMG, p. 182):
This necklace has 1d6 + 3 beads hanging from it. You can use an action to detach a bead and throw it up to 60 feet away. When it reaches the end of its trajectory, the bead detonates as a 3rd-level fireball spell (save DC 15).
You can hurl multiple beads, or even the whole necklace, as one action. When you do so, increase the level of the fireball by 1 for each bead beyond the first.
This means you can throw a whole necklace for the equivalent of an "11th-level" Fireball.
This is the because of the specific mechanic of this item; it is an exception to a general rule (cf PHB p.7 under Specific Beats General). In most circumstances you cannot upcast a spell beyond 9th level, simply because there are no 10th or 11th-level slots.
However, in this case, if you were lucky enough to get a Necklace of Fireballs with 9 beads (1d6+3), and threw the whole necklace, you would be causing damage equal to an 11-th level Fireball spell.
Fireball is already a 3rd-level spell, so adding +8 beads brings the spell to an equivalent 11th-level spell.
The damage would be: 8d6 + 8d6, or an average of 56 points of fire damage on a failed Dexterity saving throw - which is not much, considering a 9th-level spell like Meteor Swarm for instance can potentially inflict 20d6 points of fire and 20d6 of bludgeoning damage, or 140 average on a failed saving throw.
As a side note, you can do much more damage by throwing one bead at a time! Throwing them this way, a necklace with 9 beads, can potentially cause 9 times 8d6 damage, which would be an average of 252 (9 times 28) damage on failed saving throws.