Do SSRIs downregulate or upregulate the 5-HT3 receptor?
There are five subunits to this receptor (5-HT3), which are encoded by the genes HTR3(A-D) and differentially expressed depending on cell location in the (human) body. In contrast to the information in the previous answer, my first source actually has shown HTR3A to be most highly expressed in the CNS. The others are almost exclusively found in cells of the gut. 

My second source reveals that the 5-HT3A receptors are up-regulated (show increased expression) on the cell surface in the presence of agonists and antagonists to the receptor. So, if an agent was increasing the amount of 5-HT (serotonin, an agonist) outside the cell, as would an SSRI, the expression of the receptor subunit-encoding genes would be expected to increase. 


Niesler, B., Frank, B., Kapeller, J. &amp; Rappold, G. A. Cloning, physical mapping and expression analysis of the human 5-HT3 serotonin receptor-like genes HTR3C, HTR3D and HTR3E. Gene 310, 101–111 (2003).
Morton, R. A., Baptista-Hon, D. T., Hales, T. G. &amp; Lovinger, D. M. Agonist- and antagonist-induced up-regulation of surface 5-HT3 A receptors. Br. J. Pharmacol. 172, 4066–4077 (2015).