A touch 10 cannot be used with multiple codecs at once - there should be no issue with disconnecting it from one and connecting it with another - you may need to factory reset it if it continues not to work.
There may also be a hardware/software incompatibility. See the "Peripherals hardware dependencies" section of the CE9 release notes.
Depending on the codecs you are using, there may also be PoE issues - the newer codecs can provide PoE for the Touch10 directly, where some of the older ones require you use a PoE Injector between the codec and Touch10.
Without knowing which codec models or versions you are using, it's a little hard to provide more specific information.
Wayne
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