Enchanting an already magic sword

[SpicyBoi_Nezu]

My DM gave me a sword that morphs into the bladed weapon you desire the most (doesn't give proficiency) and it does 5 cold damage as well as 5 fire damage upon hitting. I was wondering if I would be able to enchant the weapon with a +1 enchantment at a normal price, because I know that stacking enchantments increases the cost of each enchantment (see +1 flaming longsword).

[Thurbane]

It might be hard to calculate with a custom weapon property: you may need to check with the DM and find out what the bonus equivalent is for the ability, or if its a flat price enhancement.

[MisterKaws]

It might be hard to calculate with a custom weapon property: you may need to check with the DM and find out what the bonus equivalent is for the ability, or if its a flat price enhancement.

I believe, per the MIC, that common enhancements to items(I.e: All Enhancement bonuses to attack/armor/saves/abilities/skills) don't require calculating the multipliers for multiple bonuses. Anyway, you can look up the rules over there.

[Thurbane]

As the OP points out, enchanting a +1 equivalent weapon with a new +1 equivalent ability is going to be cheaper than enchanting a +2 equivalent weapon with a new +1 equivalent ability.

[MisterKaws]

As the OP points out, enchanting a +1 equivalent weapon with a new +1 equivalent ability is going to be cheaper than enchanting a +2 equivalent weapon with a new +1 equivalent ability.

That's true.

That weapons seems to be some weird elemental version of Collision. Definitely homebrew, so you gotta check with your DM.

[KillianHawkeye]

Technically speaking, you can't have any magical properties on a weapon (or armor) without the item already possessing the basic +1 enhancement bonus that makes it magical to begin with. By RAW, that is always the first prerequisite.

[Crake]

My DM gave me a sword that morphs into the bladed weapon you desire the most (doesn't give proficiency) and it does 5 cold damage as well as 5 fire damage upon hitting. I was wondering if I would be able to enchant the weapon with a +1 enchantment at a normal price, because I know that stacking enchantments increases the cost of each enchantment (see +1 flaming longsword).

When you say a +1 enchantment, do you mean a special ability? Or literally a +1 enhancement bonus? If it's the latter, it should already have that, because it can't be a magic weapon without first getting a +1 enhancement. If you mean adding a special ability, then it literally comes down to "ask your DM how much it will cost, because it's a homebrew item".