Meshlab does support files with several texture files, just by using a separate material for each texture. It is not clear if you are generating your obj files with meshlab or other program, so I'm not sure if this is a meshlab related question.
Here is a sample of a minimal multitexture .obj file (8 vertex, 4 triangles, 2 textures)
mtllib ./TextureDouble.obj.mtl
# 8 vertices, 8 vertices normals
vn 0.000000 0.000000 1.570796
v 0.000000 0.000000 0.000000
vn 0.000000 0.000000 1.570796
v 1.000000 0.000000 0.000000
vn 0.000000 0.000000 1.570796
v 1.000000 1.000000 0.000000
vn 0.000000 0.000000 1.570796
v 0.000000 1.000000 0.000000
vn 0.000000 0.000000 1.570796
v 2.000000 0.000000 0.000000
vn 0.000000 0.000000 1.570796
v 3.000000 0.000000 0.000000
vn 0.000000 0.000000 1.570796
v 3.000000 1.000000 0.000000
vn 0.000000 0.000000 1.570796
v 2.000000 1.000000 0.000000
# 4 coords texture
vt 0.000000 0.000000
vt 1.000000 0.000000
vt 1.000000 1.000000
vt 0.000000 1.000000
# 2 faces using material_0
usemtl material_0
f 1/1/1 2/2/2 3/3/3
f 1/1/1 3/3/3 4/4/4
# 4 coords texture
vt 0.000000 0.000000
vt 1.000000 0.000000
vt 1.000000 1.000000
vt 0.000000 1.000000
# 2 faces using material_1
usemtl material_1
f 5/5/5 6/6/6 7/7/7
f 5/5/5 7/7/7 8/8/8
And here is the TextureDouble.obj.mtl file. To test the files, you must provide 2 image files named TextureDouble_A.png and TextureDouble_B.png.
newmtl material_0
Ka 0.200000 0.200000 0.200000
Kd 1.000000 1.000000 1.000000
Ks 1.000000 1.000000 1.000000
Tr 1.000000
illum 2
Ns 0.000000
map_Kd TextureDouble_A.png
newmtl material_1
Ka 0.200000 0.200000 0.200000
Kd 1.000000 1.000000 1.000000
Ks 1.000000 1.000000 1.000000
Tr 1.000000
illum 2
Ns 0.000000
map_Kd TextureDouble_B.png