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In this paper, we present two proposals for multi-two-party contract signing with blockchain support. In the scenario in this paper, a customer wants to purchase products/services from multiple vendors with the requirement that she wants all or none of the products. Our proposals satisfy the security requirements for contract signing: fairness, timeliness, nonrepudiation, effectiveness and confidentiality. Furthermore, one of the two proposals requires the execution of blockchain functions only in the case of dishonest behaviour (bc-optimistic). The only previous solution found in the literature for the multi-two-party contract signing scenario requires the use of a trusted third party (TTP); however, the approach is highly inefficient, requiring the exchange of many messages. Our proposals are much more efficient than the TTP-based proposal, as our proposal reduces the number of exchanged messages required to complete multi-two-party contract signing. As the use of blockchain incurs a fee, we prove the technological and economic viability of our proposals on different blockchains.