I will add a dew/temperature transmitter (Comet) to an existing flow-meters network (Micro-Motion). The flow-meters network works with 24V while the new device will work with 12V. Is it possible to work like that? Using two different power supplies? Thank you!!
Modbus is a communications protocol having nothing whatever to do with network media. Thus, your question is confusing to say the least.
Kinda sounds like you are mixing up your connections. In my experience, flow meters and other devices reporting analog values utilize current loops (4-20ma is common) connected in turn to a device that can convert the value provided into a Modbus message. Such a device could service more than one analog input device. Note the communications from the monitored device is entirely isolated from the Modbus network. Each has a different job to do.
Perhaps you are confusing Modbus with, say, RS-485 or RS-232 which are hardware communication standards. Generally, Modbus is used with RS-485. In turn, RS-485 is a differential signaling hardware protocol that typically uses 5 VDC for connectivity. Assuming (a dangerous thing, I know) that you are referring to something like this, it does not matter what primary power source the communication device uses. It will generate the requisite signal required.
You will need to make sure the two power supplies share a common ground reference (three supplies, assuming you have a third ‘master’ device for the Comet & MicroMotion).
Multi-vendor Modbus is very common, but as mentioned, it is critical the ground references are correctly tied together. In your example, if you could power the new device from the older power supply (not add yet-another supply), that would be the best least risk solution.