Hi Babak,
I do not have access to GTEX datasets, unfortunately. On my standard testing dataset I can see an increase in % of multimappers at the expense of unique mappers, though not as large as the one you observed:
sjdb Unique Multi
350k 89.29% 6.00%
2.3M 87.49% 7.71%
I looked at the reads that become multi-mappers with 2.3M sjdb, and it appears that most of them map to junctions on the mitochondrial genome.
So I generated genome excluding chrM junctions from your 2.3M set, and got:
sjdb Unique Multi
2.3M, no chrM 88.78% 6.50%
These number are much closer to the 350k sjdb case. Also, the mapping speed in this case is two-fold higher than the 2.3M with chrM case and only ~30% less than the 350k case.
Thus I conclude that at least on my dataset both the mapping slowdown and reduction in the % of unique mappers are caused in large by the sjdb junctions on chrM.
I would suggest that you generate your genome without the junctions on chrM and try to map your samples to it, hopefully the problems will be resolved as well.
I think it is to be expected that some unique mappers become multi-mappers as you add more and more sjdb junctions, since this effectively adds more possibilities for the reads to align. Note, that by default the --sjdbScore = 2, which means that STAR will try to map aggressively to the sjdb junctions, preferring spliced alignment with 1 mismatch to an unspliced alignment without mismatches. You may want to try to reduce this parameter, though it will lead to yet another slight decrease in the % of unique mappers.
Cheers
Alex