Is there a reasonable scientific backing for Carl Jung's type theories? I have read a lot on how most psychologists reject the Myers Briggs Type Indicator for its lack of scientific backing, but I have yet to find much information on the acceptance of Carl Jung's theories, specifically his idea of cognitive functions. I'm nowhere near an expert in psychology, so I could be totally off base, but in my subjective experience, Jung's ideas of cognitive functions seem to have much more explanatory power than the MBTI E/I, N/S, T/F, J/P dichotomies, and framing the theory in those terms seems to cause much less inaccuracies in typing people differently over time -- one of the reasons I've heard most psychologists reject the MBTI.

Do Jung's theories have more backing than the MBTI, or are they essentially on the same scientific footing? I get that trait-based models like HEXANO may be better in actually predicting behaviour, but what interests me about Jung's idea of cognitive functions is that they better explain motivation and modes of thoughts, which I find very personally compelling. My only fear is that explaining motivations and modes of thought would be more difficult to scientifically pose as opposed to trait-based models of personality. 

I would also be interested to know if Jung's theories do not have a solid scientific foundation, if there are similar "cognitive function" based theories that are more accepted in the psychological community.
It appears that there is little scientific backing for Jung's theories. As these theories were first suggested at the start of the 20th century they have had a considerable amount of time to receive scientific support. If they were accepted by scientists it therefore seems like they would have been widely used and cited by scholars in the interim period. 

However, if I do a search (in titles, abstracts and keywords) for related content on SCOPUS I get only 12 references (the details of which I have pasted below for you to consider). The low level of search results (and the fact that few of these appear relevant) provides strong evidence that there is little scientific support for Jung's work. 

In terms of alternative theories to consider, if I were you I would have a look at the "big five" also known as OCEAN as there is a lot more support for this personality theory. For examples of some influential and interesting articles, please see the OCEAN references section below.

References from the SCOPUS literature search:

Search term:
TITLE-ABS-KEY ( jung  "cognitive functions" )

Novak M.    Ideal types of law from the perspective of psychological typology [Idealni tipi prava v lu?i psihološke tipologije] 2013    Revus   

Lo J.-J., Chan Y.-C.    Design of adaptive web interfaces with respect to student cognitive styles  2011    Advances in Intelligent and Soft Computing

Semetsky I. Jung and Tarot: A Theory-practice Nexus in Education and Counselling    2012    Jung and Educational Theory

Connolly A.M.   Cognitive aesthetics of alchemical imagery  2013    Journal of Analytical Psychology

Naghavi H.R., Nyberg L. Integrative action in the fronto-parietal network: A cure for a scattered mind  2007    Behavioral and Brain Sciences

Sebastian A., Jung P., Krause-Utz A., Lieb K., Schmahl C., Tüscher O.   Frontal dysfunctions of impulse control - A systematic review in borderline personality disorder and attention-deficit/hyperactivity disorder   2014    Frontiers in Human Neuroscience

Segall J.M., Allen E.A., Jung R.E., Erhardt E.B., Arja S.K., Kiehl K., Calhoun V.D. Correspondence between structure and function in the human brain at rest    2012    Frontiers in Neuroinformatics

Vieira A.G., Sperb T.M. Symbolic play and the narrative organization of the child's life experience [O brincar simbólico e a organização narrativa da experiência de vida na criança]   2007    Psicologia: Reflexao e Critica

Park H.-J., Lee S.Y., Shim H.S., Kim J.S., Kim K.S., Shim I.    Chronic treatment with squid phosphatidylserine activates glucose uptake and ameliorates TMT-induced cognitive deficit in rats via activation of cholinergic systems    2012    Evidence-based Complementary and Alternative Medicine   

Seo Y., Burns K., Fennell C., Kim J.-H., Gunstad J., Glickman E., McDaniel J.   The Influence of Exercise on Cognitive Performance in Normobaric Hypoxia    2015    High Altitude Medicine and Biology  

Kwon H.G., Choi B.Y., Kim S.H., Chang C.H., Jung Y.J., Lee H.D., Jang S.H.  Injury of the cingulum in patients with putaminal hemorrhage: A diffusion tensor tractography study 2014    Frontiers in Human Neuroscience 

Lee J.H., Kim S.E., Park C.-H., Yoo J.H., Lee H.W.  Gray and White Matter Volumes and Cognitive Dysfunction in Drug-Naïve Newly Diagnosed Pediatric Epilepsy    2015    BioMed Research International   

OCEAN sample references

Roberts, Brent W., Kate E. Walton, and Wolfgang Viechtbauer. "Patterns of mean-level change in personality traits across the life course: a meta-analysis of longitudinal studies." Psychological bulletin 132.1 (2006): 1.

Hayes, Natalie, and Stephen Joseph. "Big 5 correlates of three measures of subjective well-being." Personality and Individual differences 34.4 (2003): 723-727.

Kotov, Roman, et al. "Linking “big” personality traits to anxiety, depressive, and substance use disorders: a meta-analysis." Psychological bulletin 136.5 (2010): 768.