Corinthians face an uphill battle to progress to the quarter-finals, while Internacional are well placed to advance.
Corinthians must overturn a two-goal deficit if they are to prolong their Copa Libertadores campaign beyond the round of 16.
Adenor Leonardo Bacchi's team trail Paraguayan outfit Guarani 2-0 heading into Wednesday's return leg in Sao Paulo, Brazil.
Corinthians conceded two goals in the second half to leave themselves with a mountain to climb in their bid to join Tigres UANL, who are the only team so far to progress past the last-16, in the quarter-finals.
The 2012 champions, however, head into their second leg against Guarani on the back of a 1-0 victory over reigning Brazilian Serie A champions Cruzeiro in the opening round of their domestic league on Sunday.
"I accept any result if the opponent is better than me. It is a football game, it's not kill or be killed," Bacchi told reporters.
"Guarani can come here and win. What I ask is the performance of normality. Resume standard to be better than your opponent."
Fellow Serie A outfit Internacional are in a much better position as they prepare to host Atletico Mineiro in an all-Brazilian affair on Wednesday.
Inter scored two priceless away goals in a 2-2 draw at Mineiro last week.
Twice Inter took a lead, and twice they were pegged back by Mineiro in an entertaining first-leg battle.
Since leaving Belo Horizonte with the tie balanced in their favour, a second-string Inter team were swept aside 3-0 by Atletico PR on Sunday.
"The Libertadores is the ultimate dream. Everyone wants to advance," Inter coach Diego Aguirre said.
"We do not neglect the Brasileirao [Brazilian Serie A] but the priority is Wednesday. We took a risk. It [the defeat to Atletico PR] happened."
Brazilian giants Sao Paulo are also in action on Wednesday, travelling to Cruzeiro with a 1-0 lead.
River Plate, Emelec and Estudiantes all take leads into their second-leg matches.
Thursday will see River make the trip to bitter Argentine rivals Boca Juniors following last week's hard-fought 1-0 victory on home soil.
Ecuadorian side Emelec face Atletico Nacional in Colombia on Thursday, with the former leading 2-0.
Estudiantes of Argentina hold a slender 2-1 advantage over Colombia's Santa Fe heading into Tuesday's showdown.
Meanwhile, Racing Club host Wanderers on Thursday with the tie poised at 1-1.