You can have a maximum of 10 treaties, standard. However, by researching Xeno-Diplomacy in the Base research branch, you can unlock the Embassy module for your base. Each Embassy adds 2 to the max treaties you can have, up to a limit of 5 Embassy mods. So, if you sacrifice the necessary Special Space on your base to allow for 5 Embassies, you can have a total of 20 treaties.
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[20:40] Wredz: just hacked a massive extremely rich minting planet from someone.. thats the best planet i ever hacked
[20:43] DarthFlagitious: is it spearmint or peppermint?