Trying to avoid self-joins - need a different approach??

[Norman Bethe]

I have a table that has values of variables for certain entities. The
columns of interest are targetID, variableID, and valueID. A row (1, 5,
9) means that target number 1 has a value of 9 for variable 5. Being
denormalized, target number one will have many possible rows in this
table, one for each variable for which it has a value.

My problem occurs when I want to find out what targets match a certain
set of variable values. For instance, I want to find out what targets
have a value of 9 for variable 5 and a value of 25 for variable 10. I'm
thinking that this can be a simple self-join:

SELECT mya.targetID from mytable as mya
LEFT JOIN mytable as myb
ON mya.targetID=myb.targetID
WHERE (mya.variableID=5 AND mya.valueID=9)
AND (myb.variableID=10 AND myb.valueID=25)

Does this make sense so far? The problem is that this doesn't scale.
When I have more than 31 variables and I need to evaluate them all,
MySQL breaks: I can't do more than 31 joins.

My design calls for perhaps 80-100 variables, so even 64-bit
architecture with a limit of 64 joins won't get me there. This is NOT
an architecture or platform issue - I need a design and a data
structure that will scale to lots of variables.

I need another data structure that won't get me stuck on too many
joins. Any suggestions? If I have to scrap this approach in favor of
another, I can do that; even some clues on what direction to head out
on would be helpful. I'm stuck at the present. Thanks.

Oh, and if I should post this somewhere else, please let me know.
There's a copy of this on mailing.database.mysql.