A reader wrote to me and stated that he had “harsh Multiple Chemical Sensitivities” and this improved it greatly. While this is an anecdotal report, I do like following up on such (to see if there is logic to it via the model that I am working from).
On MCS sites and books, it is often sited as being needed, for example:
But in “University of Toronto case–control study of multiple chemical sensitivity-3: intra-erythrocytic mineral levels ” Molybdenum was detected in only 7% of the MCS suffers (and only 7% of the controls!) with both groups being 200 people. The level was much lower for this 7% (0.021 vs 0.077) but for 93 percent of each group, it was not detectable.
There was very few hits on PubMed,
- “Results of this study suggest that Cu from CuGly may be more available than CuSO(4) when supplemented to diets high in S and Mo.” 
- “molybdenum-induced secondary copper deficiency… illness and subsequent death of cows was observed. ”  – do NOT overdose on this supplement!!!!!!!! More is not better, more may be deadly!
Thus supplementation could reduce copper levels — unfortunately, the studies that I found had MCS and CFS having normal copper levels (as a population) compared to controls, so this is unlikely to be the mechanism of action for MCS relief.
The microbiome dimension
- “Intakes of copper, magnesium, manganese, and molybdenum were positively associated with Firmicutes (r = 0.33, 0.38, 0.44, and 0.51, respectively; P ≤ 0.01) and negatively associated with Bacteroidetes (r = -0.38, -0.44, -0.48, and -0.53, respectively; P ≤ 0.01).”  Note: molybdenum had the greatest effect of the four minerals.
- ” In contrast, in the stool samples there was a higher relative abundance of Bacteroidetes and lower abundance of Firmicutes observed in ME/CFS patients compared to healthy controls.” 
- “In certain gastrointestinal disorders, however, extensive fecal losses may occur. Balance data obtained in our laboratory from two subjects with Crohn’s enterocolitis demonstrated that during active disease, gastrointestinal losses of molybdenum may exceed 400 ,ug/day.” 
The traditional rationalization of for taking molybdenum (low levels) does not stand up to studies. There are no studies of molydbenum with IBS/FM/CFS (which is always my gold standard).
According to the model, molybdenum should help shift ME/CFS microbiome in the right direction. All of this literature is from 2015.
If you take it, keep to the recommended dosages and consult with your knowledgeable medical professional.
As a further FYI: he used Thorne Research – Molybdenum Glycinate – Trace Mineral Cofactor – $9 for 60 capsules