Which 3 Line Phone?
Finding a cordless 3 line phone is more than a challenge. The few options that were available now appear to have been discontinued. The latest casualty is the Panasonic KX-TH102-M
3-Line Digital Expandable Cordless System. It's was high end solution with loads of features.

The majority of multi line phone systems are either 2 or 4 line units. Prospective buyers regularly end up with a
4 line cordless phone and are not unhappy with having a spare line in reserve.
The most important factor in selecting a multi line phone system is to get a unit that has the right cordless phone frequency, i.e. 5.8 GHz or DECT 6.0. Recently released two line DECT 6.0 phones such as the Panasonic KX-TG9391T are proving to be at least as good as 5.8 GHz phones - more information.
See: Cordless Phone Frequencies
Three line corded units are a less expensive option, but potentially a false economy if new or additional wiring is required.
Recommendation
A 3 line business phone whether corded or cordless is usually not a good investment. An option that will provide greater flexibility over the long term is a 4 line cordless phone such as the Panasonic KX-TG4500B. It is manufactured to meet business specifications and is expandable through to eight handsets. As it's cordless there are no wiring or installation costs.
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