In the immunotherapy based on immune checkpoint inhibition (IC), additional ICs are being studied to increase its effectiveness. An almost unstudied feature is the possible co-expression of ICs, which can determine the therapeutic efficacy of their inhibition. For the selection of promising ICs, information on the association of their expression with cancer development may be essential. We have obtained data on the expression correlation of ADAM17, PVR, TDO2, CD274, CD276, CEACAM1, IDO1, LGALS3, LGALS9, and HHLA2 genes in gastric cancer (GC). All but one, TDO2, have other IC genes with co-expression at some stage. At the metastatic stage, the expression of the IDO1 does not correlate with any other gene. The correlations are positive, but the expressions of the CD276 and CEACAM1 genes are negatively correlated. The expression of TDO2 and LGALS3 is associated with GC metastasis. The expression of TDO2 four-fold higher in metastatic tumors than in non-metastatic tumors, but LGALS3 was two-fold lower. The differentiation is associated with IDO1. The revealed features of TDO2, with a significant increase in expression at the metastatic stage and the absence of other IC genes with correlated expression indicates that the prospect of inhibiting TDO2 in metastatic GC. IDO1 may be considered for inhibition in low-differentiated tumors.