Here's my guesses, bearing in mind that the weapon has to be the same:
Gladiator + Pugilist = Thief
Gladiators have access to daggers. Since Paladin is a low dd, single-target tank, it'd make sense to give them some dd potential. Especially for during fights where a warrior is the ideal tank.
Lancer + White Mage = Templar
In Tactics, Templar was a heavy armor spear-wielding enfeebler. Since Arcanist is the only other true enfeebler, as I remember SE describing it, then Templar could fill an under-utilized party roll.
This could sort of focus on "white" enfeebles with the theme of movement. Paralyze, slow and bind.
Warrior + Thaumaturge = Dark Knight
Not the scythe for which some were undoubtedly hoping; but nonetheless a big axe and black magic!
Turn that AoE tank into a single-target dd. I think, in the sake of keeping things interesting, they should make it so the DK buffs their weapon with potent, but self damaging, buffs.
Like a fire enchant that burns the user slowly draining hp but gives a large strength boost.
Pugilist + Thaumaturge = Sage
Hand-to-hand is a tough one. In Tactics Advanced 2, Sage was able to use white and black magic, and monk abilities. While in most other games they're relatively weak, TA2 made them a bit stronger with the addition of monk abilities.
This could turn them into something of an AoE dd along with enfeebled like Bio and some large damage melee attacks.
Conjurer + Arcanist = Green Mage
Not much of a departure from their healer toll as white Mage, but Green has some potential as a pseudo time Mage. Their spells include accuracy and speed bonuses while adding in some minor dd.
Thaumaturge + Arcanist = Time Mage
The Yin and the Yang. Where green Mage speeds up and buffs the party, Time Mage slows and debilitates the enemy.