Incomplete transactions are invalid, and invalid transactions do not propagate over the network, so you cannot broadcast an incomplete transaction for later modification by another user.
Incomplete transactions can be shared out-of-band (e.g. on message boards) via Partially Signed Bitcoin Transactions (PSBT). if The inputs and outputs of the transaction creator are SIGHASH_SINGLE | SIGHASH_ANYONECANPAY construction. A second participant can enter the remaining inputs and outputs to further achieve the intended result.
However, if you want to allow two participants to both input into one output script, the protocol requires at least one round trip because the original transaction creator cannot sign off on an incomplete output script. Therefore, either the second participant can unilaterally determine its output, or the second participant must make changes and then return the transaction to the creator.
Honestly, I don’t fully understand what you’re trying to accomplish, so I may be missing some workarounds or tricks, but the above should cover common situations. Your problem reminds me of how Inscription Marketplace uses PSBT to offer NFTs for sale. If you’re not familiar with it, it might be interesting to research that approach.
If you want to better understand how HTLC works, you might want to check out Elle Mouton’s excellent HTLC Deep Dive. Her other blog posts may also be of interest in the context of your research.
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