A software wallet application or coordination software initiates a multi-sig wallet, choosing the number of total keys, and the number required to sign transactions. You then add private keys from other wallets generated elsewhere to the multisig after which the software wallet can complete the creation process. For any future transaction from the multi-sig wallet the required amount of co-signers need to sign (using Partially Signed Bitcoin Transactions - PSBT from [BIP174](https://github.com/bitcoin/bips/blob/master/bip-0174.mediawiki)) before any transaction is valid.
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