Yellow is based on sight. Thematically, it trusts what it sees and manipulates what others see; but that leads to problems when there's internal struggle, as they begin to trust things that are not what they seem. Mechanically, this might perhaps be represented by, for example, clones, color-changing/color-matters, type-changing/type-matters, transform cards, illusions, etc. Or something else--be creative!
Brown is based on hearing. Thematically, it trusts what it hears more than what it sees. This allows it to know certain things are happening even when it's not looking at them, but it also means when things are quiet, it's vulnerable. Mechanically, brown may do things like ignore buffs (they can hear what's under the visual tricks), flash in blockers (they can hear the enemy coming and prepare for ambush), etc.
Purple is based on touch/feeling. Thematically, it doesn't trust anything until it's got it in its hands. Similar to the existing red, purple is aggressive. It hits first and doesn't ask questions, because once it's made contact, it doesn't have any more questions. Mechanically, it's all about combat: asymmetrically high power and toughness (so 1/5 or 5/1 might both be common purple stats), attack triggers, block triggers, the whole nine yards of combat love.
Pink is based on taste. Thematically, it's big on eating. It'll eat just about anything, living or dead, safe or dangerous. Mechanically, it's very removal-focused: exile and destruction, often for buffs, and from just about any zone imaginable. It's like the removal of white and black had a child together. It also sometimes digests its victims and returns them broken, i.e. replaces a removed creature with a weaker or detrimental version in token form.
Orange is based on smell. It relishes in odors that would make others vomit, and often it relishes in the stench of their vomit as well. Mechanically, orange is big on withery things: -1/-1 counters, -X/-X effects, etc. It sometimes also scares away others with its stenches, leading to temporary removal (i.e. bouncing or straight-up flickering). And as the sense most tied to memory, orange is also the color of recursion, bringing spells back from the graveyard and even, when powerful enough, creatures. (Thanks to GG Crono for the memory suggestion!)
*Purple vs Brown/Yellow
*Pink vs Brown/Orange
Yellow vs Orange/Purple
Brown vs Pink/Purple
*Orange vs Yellow/Pink