The Seanchan want to get rid of the Shaido, the people in the countries they're annoying want them gone, and Perrin isn't okay with just freeing Faile:

“A puzzle to solve, Faile to free, and the Shaido to destroy. That was all that mattered in the world.”

“He would not pay these Shaido for making Faile suffer. She would be afraid, and they had to pay for that, not profit from it.” (COT 8)

I think he will probably use some sneaky way to free her, and then attack the Shaido. He's horribly outnumbered right now, but I think every military group within 400 miles will become involved in this.

Location for Perrin, Shaido, and Seanchan: Perrin crossed the river Eldar into Altara, and followed the Aiel east on foot for some days (COT 5). Elyas finds the Aiel in ridge country nearly forty miles away to the northeast. (COT 8). And one of the Aiel mentions mountains to the east. If you look at the normal map in the books there are small mountains in North Altara. Perrin hasn't mentioned cross the main road going across North Altara or the main road that Mat is on.

How/why I think the groups will be involved:

The Whitecloaks: Asunawa wants to move east right into the same area: “Not so far if we move east, across Altara, my son, across the north of Altara. The Seanchan cannot have moved far from Ebou Dar yet.” (Cot Prologue). We don't know yet what they decided, but Whitecloaks have been rumored close to Perrin's group. Asunawa wants to move east because there is an army in Murandy. He doesn't even know who it is and wants to go there. They'll probably run right into the conflict and fight anyone they can see because they won't be able to decide who is more darkfriend.

The Band of the Red Hand: “I have . . . felt . . . something, for weeks now. Others in the Band have, too.

Not urgent, but always there. As if he needed me. As if I should look south, anyway. It can be peculiar, following a ta'veren.” (POD 18). I think they'll start moving toward Mat, or already have. I also think when they get closer they'll be able to tell if he suddenly veers off a few miles west.

Brotherless: They're mad at the Shaido for abandoning Ji'e'toh, and the Shaido don't like them. “None of the Shaido really trusted them, and the Brotherless themselves often seemed like men holding their noses, accepting what they considered a lesser wrong rather than embrace a greater, but no longer truly sure that it was lesser.” (COT 9). I think Faile will help Rolan toward the decision to rally them against the Shaido or at least leave.

Masema: His men will probably help against the Shaido. “‘Killing Aiel savages is doing the Light's work.' His eyes flickered toward the Wise Ones, and his smile was even colder than before. ‘I would appreciate the help, Perrin lied.' That rabble would be useless against Aiel. Still, they numbered in the thousands. And they had held off armies, if not armies of Aiel. A piece of that puzzle in his head shifted.” (WH 6)

Mat: Valan isn't going to worry about getting caught anymore now that he has the letter from Tuon. I think Mat, Thom, Juilin, the redarms, the AS and warders, the sul'dam, Egeanin, Domon, Selucia, Tuon, and Setalle will go on horseback now. In Lord of Chaos Perrin thought 35 miles in a day was good for a larger group than Mat's would be, and Mat hasn't seen snow yet, so he'd be able to move fast at the start. I think when they get close they will hear rumors of the Manetheren banner and want to know what it's about, and be drawn to Perrin. Perrin has thought of how fast news travels of it “‘I heard that you let the Red Eagle stay.' Perrin very nearly jumped. Even for just around the hill, news had traveled fast.” “Berelain would have to know the truth, yet if too many knew, that truth would spread from the next village they passed, the next farm.” (POD 9) This was when they were moving. Now they will be stopped for awhile.

Karede: I think he'll catch up to Mat when they're almost to where Perrin is. I think Tuon will decide not let them kill Mat, and they'll have heard of the 15,000 Seanchan. If Tuon wants to get to Ebou Dar fast, she might as well just go with Mat and order the DW Guards to follow because there will be to'raken there that can move 200 miles in a day. If they are close to Perrin, that would be faster than going back on Karede's horses. In fact, even if they don't hear of Perrin's army at all, they'll hear of the Seanchan for sure and even if Tuon decides to make Mat da'covale, they would probably still go closer to the Seanchan army to taken a to'raken. Then they will hear of Perrin's army and Mat will find some way to help out. (If Tuon finds out about the letter Perrin has from Suroth, and finds out it was originally given to Masema and his Dragonsworn, she will not be best pleased with her. But that is beside the point of this theory)

Total numbers in the armies:

56,000 Shaido (excluding Brotherless)

About 500 female channelers

62,200 in “Other armies” (including Brotherless)

30+ f. channelers

2 male channelers

[48,200 “Other” (excluding Brotherless)]

[70,000 Shaido (including Brotherless)]

70,000 non gai'shain Shaido (COT 9):

including about 14,000 Brotherless (POD 11, LOC 55)

About 500 Wise Ones & Apprentices (COT 8)

2,100 Perrin:

900 Winged Guards (POD 8)

900 or so Ghealdanians (POD 10)

less than 300 Two Rivers bowmen (WH 8)

about 25 Maidens, 6 Wise Ones, 3 Aes Sedai, 3 Warders, 2 Asha'man, Gual, Aram, & Elyas

12,000 Masema (COT 5)

15,000 Seanchan (COT 27):

at least 12 damane and some freaky animals

120 Karede (COT 4):

100 Death Watch Guard and 20 Ogier

6 damane

Mat: 3 Aes Sedai, 7 Redarms, Thom, & Juilin, (Aludra?)

9,000 Whitecloaks

10,000 Band of the Red Hand

So, still.. it's gonna be.. difficult. Here's some other stupid stuff. Edge just means if 5 of group A can kill 10 of group B, they have the edge.

Small Edge for Shaido: “He had fewer than two thousand lancers, and they would have been overmatched against an equal number of Aiel” (COT 8)

Big Edge for Other: “Fewer than three hundred Two Rivers men, who could wreak havoc with their bows” (COT 8)

Big Edge for Shaido: “That many Shaido would shred Masema's murderous rabble like a cat slaughtering a nest of mice” (COT 8) But if Masema gets killed then good.

Small Edge for Other: Seanchan have scary monsters.

Small Edge for Other: Band of the Red Hand with Mat's luck

Big Edge for Other: AS and Rand's Wise Ones because they know how to link.

Big Edge for Other: Asha'man. The 2 could probably kill lots of WO. Maybe they could become gai'shain and assassinate some before the real battle.

Huge Edge for Shaido: There are way too many WO. I don't see how they will be defeated unless they run because they're pissed that Sevanna got them into this mess by staying where they are.

Equal: Damane and Shaido Wise Ones. Both sides are strong and neither can link

Big Edge for Shaido: Whitecloaks. Gaul took out 7 or 8 by himself.

Huge Edge for Other: Mat and Karede are great generals.

Perhaps a tiny Edge for Other: Wetlander Gai'shain. Maybe a few of them will want to take revenge? At the least they'll try escaping and cause more chaos.

Small Edge for Other: DWGuard Ogier

Edge for Other: Shaido don't expect an attack and Sevanna underestimates the Seanchan and their “lizards”