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Or every transaction consists of only one sending wallet and one receiving wallet.

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A transaction is composed of inputs and outputs.
The inputs are the funds that go into the transaction, they can be from multiple wallets as long as every input (an input is an output from some previous transaction) is signed for by its owner.
On the output side we can send funds to any number of addresses (we are limited only by transaction size in KB)
So yes, it is possible to do just that.
As a practical example look at CoinJoin which is a way to combine inputs from different wallets together.
Hope this helps.

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    Can one do this in Bitcoin Core? It would seem not because isn't signrawtransaction bound to a particular wallet?
    – Geremia
    Jul 25, 2017 at 0:58
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    @Germania, It is possible. instead of sending the transaction to the network, you send it to the next person who will add their inputs and outputs and sign them as well, and so on. The last person would then broadcast the transaction on the network.
    – Albert s
    Jul 25, 2017 at 4:17
  • So basically I need to specify this argument of signrawtransaction: "The second optional argument (may be null) is an array of previous transaction outputs that this transaction depends on but may not yet be in the block chain"?
    – Geremia
    Jul 26, 2017 at 21:15
  • How exactly does one make a transaction using inputs from different wallets?
    – Geremia
    Nov 2, 2017 at 16:45

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