The South African champions are fighting to win silverware on three fronts, with Baxter's side remaining in contention for Premier Soccer League and Nedbank Cup titles.
A run of four games in 11 days, starting on Wednesday, is set to pose a stiff test of the Chiefs, but Baxter will not take any competition lightly, stating that "prioritising is dangerous".
"If I go out and say we will field a reserve team in the Nedbank Cup, people will hang me," he told KICKOFF.com .
"If I say we are not really bothered by CAF then people will say you are a lunatic, you are disrespecting South Africa.
"If I was to say I couldn’t care less if we win the ABSA Premiership it will be the same. So how do you prioritise?
"We just have to admit that every game is vital."
The Chiefs have been in fine form ahead of their meeting with Congolese side Vita, scoring 11 goals in four Champions League games.
Holders Al Ahly will look to maintain their hopes of securing a ninth title by making it past Ahly Benghazi.
The sides meet in Libya on Sunday, while Al Ahly's Egyptian rivals Zamalek - who missed out on qualifying from the group stage last year - travel to Nkana of Zambia.
Last year's beaten semi-finalists, Coton Sport and Esperance de Tunis, face away trips in the first leg as they travel to Entente Setif and Real de Bamako respectively.
After winning the CAF Confederation Cup for a third time last year, CS Sfaxien have made a strong start to life in Africa's premier club competition and can bolster their hopes of making the group stage with a first-leg win over Horoya of Guinea.
Sewe Sport came through a closely-fought encounter against BYC last time out, triumphing 4-3, and will hope for a smoother ride against TP Mazembe, while Sudan's only representatives Al-Hilal take on Leopards de Dolisie.
