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During FCC (or any other EMC) testing, the manufacturer will use some antenna(s) and only those antennas will be the ones approved. If you modify the antenna or use one which wasn't used in the test, then the item is no longer conforming.

Similarly, if a products housing serves as signal/chassis ground (for an antenna or similar), then you can't change the housing either as that will affect the EMC approval.

Either way, a new EMC test is likely required.

I theory you could be facing fines if you modify a product like this and it ends up disturbing other approved devices. In particular if you are a commercial company putting modified products on the market. 

FCC or equivalent authorities are probably not prioritizing chasing down hobbyists, but that too can happen. As an anecdote, this actually happened to me once. During development of a radio product, we purposely had it transmitting at larger power than allowed on the band and left it on day and night for logging/reliability testing. This eventually resulted in a sudden visit from black van with lots of curious antennas on top, belonging to the radio authorities - we had been jamming some poor soul in the same city trying to legally use that same frequency. They realized we were doing R&D work however, so they were quite understanding and we didn't get fined, but we had to dismantle our little test rig and promise not to be naughty again.