No phone answering machine will be able to answer while you are on the line. That's impossible. You might be thinking of call waiting, which lets you see the caller ID of the second caller, and you can press flash to switch to the other caller. But an answering machine would not do that. And if it could, you'd lose the connection to the first caller.
The only way to have a system that answers calls and takes messages while you are on the line is if you use the phone company's voicemail. This is a service that runs on their end, so it can handle calls without you losing the connection.
The Panasonic phone I reviewed in my article will support phone company voicemail as I mentioned in the article. You will not need a phone with an answering machine if you decide to use their voicemail, since the voicemail will answer, play your greeting and take a message.
If this is important to you, then talk to your service provider about getting their voicemail feature added to your service.