We study signals for the production of superparticles at the Fermilab Tevat
ron in supergravity scenarios based on the grand unified group SO(10). The
breaking of this group introduces extra contributions to the masses of all
scalars, described by a single new parameter. We find that varying this par
ameter can considerably change the size of various expected signals studied
in the literature, with different numbers of jets and/or charged leptons i
n the final state. The ratios of these signals can thus serve as a diagnost
ic to detect or constrain deviations from the much-studied scenario where a
ll scalar masses are universal at the GUT scale. Moreover, under favorable
circumstances some of these signals, and/or new signals involving hard b je
ts, should be observable at the next run of the Fermilab Tevatron collider
even if the average scalar mass lies well above the gluino mass.