Gardner's model actually resembles more "differential psychology", like FFM and 16PF than "hard" type theories like Myers-Briggs and Enneagram.

Gardner talked about "multiple intelligences", which seem to be correlated with socionic IM elements (not really sure) :

Linguistic -
Logical-mathematical -
Spatial -
Bodily-kinesthetic -
Musical -
Naturalistic -
Interpersonal -
Intrapersonal -

Gardner doesn't really talk of types, but more on scales ; according to him, each individual has a "cognitive profile".