We study the performances of a world-wide network made by a European third-generation gravitational-wave detector, together with a 40 km Cosmic Explorer detector in the US, considering three scenarios for the European detector: (1) Einstein Telescope (ET) in its 10 km triangle configuration; (2) ET in its configuration featuring two 15 km L-shaped detectors in different sites, still taken to have all other ET characteristics (underground, and with each detector made of a high-frequency interferometer and a cryogenic low-frequency interferometer); (3) A single L-shaped underground interferometer with the ET sensitivity curve, either with 15 km or with 20 km arm length. Overall, we find that, if a configuration with two widely separated L-shaped detectors (‘2 L’) should be retained for ET, the network made by a single-L European underground detector together with CE-40 km could already provide a very interesting intermediate step toward the construction of a full 2 L+CE network, and is in any case superior to a 10 km triangle not inserted in an international network. We also study the performance of a network made by a single L-shaped underground interferometer with the ET sensitivity curve together with a single 40 km CE and with LIGO-India (taken at A$^\#$ sensitivity), and we find that it also has very interesting performances.