I think you are:
ACME - the generic company from Looney Tunes.
My first twice flies you
My second twice puzzles you
My third twice measures you
My fourth twice tests you
Taking each letter twice:
AA = American Airlines (who 'fly you')
CC = Cryptic crossword (which 'puzzles you')
MM = Millimetre (which 'measures you')
EE = Entrance exam (which 'tests you')
ASCII from my first,
Shaped like my first,
Anchored on my first,
Misses 1 of my first
This describes the drawing of a letter A ('Shaped like my first') using component letters ('from my first'), like this:
A
C C
M M
E E
Note it is 'anchored' on two A's, but is missing a character to draw the horizontal line across the middle ('1 of my first').
Catching a loss,
I become my head;
Taking two more,
A triangle instead
If we 'catch a loss' - add an L - then the shape becomes a complete A ('my head'):
A
C C
M L M
E E
If it then 'takes two more' in the bottom row, we get 'a triangle instead':
A
C C
M L M
E L L E
When filled as so,
My third row's a scheme;
And then, my end,
A French magazine
An MLM strategy (from row 3 of the triangle) is a multi-level marketing scheme. Elle (row 4) is 'a French magazine'.
My first remains quite solitary;
Like I too it has matches nary
My products made can be quite scary;
When defective, effects may vary
Back to a typical riddle! 'A' is the indefinite article for a singular ('solitary', with 'matches nary') object. And in Looney Tunes the ACME products tend to be traps ('can be quite scary') used by Wile E. Coyote for catching his nemesis, Roadrunner. But do they ever work??! No! ('defective, effects may vary')
As for the title:
Not only is ACME a company, but the word 'acme' means 'peak', 'top' or 'best'...
