aspect N4 common casualpolitewritten
〜ていて — て-form of いる joining clauses ('is ~ing and...'
〜ていて ・ ていて
Builds on ている
A full written guide for 〜ていて is on the way.
This point is mapped in the grammar tree, but its examples, formation table and usage notes haven't been written yet. The fastest way to learn it now is to meet it in real sentences inside Jengo.
See 〜ていて in real sentences
Jengo shows 〜ていて the way you actually meet it: inside real Japanese sentences, so it sticks instead of staying an abstract rule.
Study it in JengoSources Compiled with reference to A Dictionary of Intermediate Japanese Grammar. Editorial confidence: low.