If you take twelve randomly generated words and combine them with twelve different randomly generated words you don't exactly double your entropy. First of all, electrum doesn't generate or imports 256 bits of entropy, but only 128, that's why it returns you only 12 words.

Each electrum seed is already extended with the word “electrum”, if you choose to extend it more with another seed phrase it'd become “electrum<seed_phrase>”. So it doesn't double the entropy, instead, the entropy remains the same. What it does change is a salt. Once you're done with the seed generation and salt selection, the result is being put through a key derivation function called “PBKDF2”. But, you can of course do it, it'll provide the same security*.

*Geek alert! Not exactly the same. You see, once you generate an electrum seed the twelfth word isn't randomly chosen from those 2048 words due to the checksum. So, in your 24 words, the twelfth and the twenty fourth words won't be same like predictable as the rest of them.

Yes, but whether you lose the extension or the seed, you'll lose your money.

Is there any specific reasons why you want that method? Goin' with electrum's 136 bits is more than fine.

If you need to divide up the responsibility for possession of your funds among multiple people, you should use multisig, otherwise the 12 words are more than enough.