Why not? The original job from FFXI had both elements, and one mechanism that was pretty useful was using main hand weapons like Joyeuse to build TP and doing weaponskills with gun.

Here's me haphazardly daydreaming how some abilities might work

Lv 1 - Lunge - Deals 140 dmg to target in range.
Lv 2 - Slow Fire - Deals 140 dmg to target at a distance.
Lv 4 - Piercing Mark - Deals 100 melee damage to target, Combo Bonus (Lunge)- 180 dmg. Grants 10% Bonus to Party's Ranged Attacks.
Lv 6 - Crippling Fire - Deals 100 range dmg to Enemies in Cone. Grants 10% Bonus to Party's Melee Attacks
Lv 8 - Shuffle - Gives party buffs based on next 3 attacks executed - (Card Animation)
Ex. Range + Range + Range = Critical Hit Bonus 5%
Ex. Melee + Melee + Melee = Determination Bonus 5%
Ex. Melee + Melee + Range = Magic Damge 5%
Ex. Range + Range + Melee = Physical Damge 5%
Ex. All other combinations = Random effect.
Lv 10 - Double Shot - Deals 100 Damage to ranged target - Combo Bonus (Slow Fire) - 200dmg.
Lv 12 - Quick Draw - Fires non-elemental damage from pistol for 150 (off GCD)
Lv 15 - Accomplice - Causes enmity generated to be given to player in mob's line of sight.

I kinda stopped my fanboy rambling at lv 15, but i think you can see where I was going. It's a party buffing melee/range that can do either exclusively, or combine the two for better outcomes. A big chunk of it's damage is generated by the other members of the party.

Any thoughts?