I very appreciate it, Dr. Gang.

When I code with + or * the error does not change:
3dMVM -prefix COMPARE_masked_all3 -jobs 1 \
-bsVars 'group+class' \
-SS_type 3 \
-num_glt 3 \
-gltLabel 1 G1_vs_G2 -gltCode 1 'group : 1*G1 -1*G2' \
-gltLabel 2 G3_vs_G2 -gltCode 2 'group : 1*G3 -1*G2' \
-gltLabel 3 G1_vs_G3 -gltCode 3 'group : 1*G1 -1*G3' \
-mask mask_resamp_bin+tlrc. \
-dataTable @dataTable_new_covariate.txt

However, following the point you attracted my attention to, I started changing the way I used to code my dataTable. I have three groups: G1, G2, and G3. G2 and G3 are paired datasets. So, for the variable class, I coded every single member of G1 differently (e.g., NR1, NR2, NR3, ..., NR32), and labeled members of G2 and G3 with paired coding (G2: T1, T2, ..., T21) and (G3: T1, T2, ..., T21). The new coding method seems more meaningful than the way I had coded them in the past. The same error is still there though. What I can notice is that I have many 0 values between parameters G1, G2, G3 and the parameters of the covariate named class, which from this perspective is similar to the same issue that you highlighted.

May I ask if there are any other ways of formulating the model that you might recommend?

Thank you so much for your time.

Respectfully,
Sanaz