The Rangers boss revealed that both Francesco Stella and Sebastien Faure had trained and played well in a closed-door game at Auchenhowie earlier this week.
And joining that pair in training today were a Greek defender and an Argentinian midfielder.
24 year-old Anestis Argiriou featured recently for AEK Athens and has represented his country at under-21 level.
He can play as either a right sided full back or a central defender and previously had trials with Blackburn under Sam Allardyce.
Francesco Celeste is a left sided midfielder formally of Boca Juniors in his homeland.
The pair were put through their paces along with French defender Faure, who McCoist admits he is hopeful of striking a deal with, and Stella, a 21-year-old Italian-Australian.
Formerly of South Melbourne FC, he left for Italy where he joined Siena before spending time on loan in the lower leagues in Italy.