I had created my own cognitive functions MBTI test, based on Sum Typing (I plan to post about Sum Typing soon). This is a quite innovative and different MBTI quiz/test, based mostly on cognitive functions. This quiz uses a big collection of stats of my own, some of them indirectly accessing the 16 MBTI/Jung types rather than directly (E/I is deducted quite indirectly), with interesting questions. It uses the Sum Typing method, being supplemented with some E/I dichotomy questions (that are very discrete, some of them doesnt even seem to relate with E/I) and a few questions that access type directly, two of them related to Truity and some few inspired on Sakinorva Cognitive Functions test.
This also takes advantage of Big 5 and Enneagram connections with MBTI, so, one can expect a few questions related to Enneagram and Big 5 on a MBTI test, which is quite innovative! I had done this test before creating Typology Triad, so it is on an external link:
https://www.quotev.com/quiz/12501474/Sum-Typing-MBTI-Test-with-cognitive-functions
Have fun =)
EDIT (2021): I had also created a test more proper and true to Jung Typology:
https://www.quotev.com/quiz/13472609/Jung-Typology-Test
You can also check other tests from me here:
Typology Triad 
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