If you want to define something that does not exist then you also have to define a standard for it too. For example in this case you can define it like this:
1. Append all the transaction outputs you want to sign together. (Lets assume it is 5 UTXO belonging to 3 keys). Put transactions that belong to one key together and the order is important.
[Tx1_key1][Tx2_key1][Tx3_key2][Tx4_key3][Tx5_key3]
Perform a SHA256 on the whole thing to make it 32 bytes.
2. Sign with key1, key2, key3 and then concatenate 3 resulting signatures together. You can DER encode it if you like:
[Seq][size]
[Seq][size][int][size][r][int][size][s]
[Seq][size][int][size][r][int][size][s]
[Seq][size][int][size][r][int][size][s]
* Seq and int are DER flags.
** There is an additional part in signatures for recovering public key that I am not familiar with yet but assume we added that to the signature