Acutally you can; my brother is doing it with a friend, but it's tricky. It's like buying plus, having your account on both devices and interchanging devices with someone else.
Take: Skynet (my brother's PS4), and Cerebro (his friend's); Charlie (my brother's account) and David (his friend's).
There's an option in the PS4 that says something like: "Activate Device" for "Game" and for "Video", to activate a main account on the device.
David has Plus privileges on his account but his 'Active Device' is Skynet, and vice- versa Charlie has Cerebro as his main device. And they both have their accounts on both devices (main and secondary).
So on Cerebro are both accounts, Charlie and David. Charlie is the main account of that device but it's on David's house; and on Skynet too are both accounts, David is the main account, and it's in Charlie's house.
Basically David+ is playing with his account on Charlie's device, in his own house (as if he were a guest in his own device), and Charlie is playing in his house, with his account on David+'s, device.
Cerebro (in David+'s house): Skynet (in Charlie's house):
> -Charlie (Main) -David+ (Main)
> -David+ (2nd) -Charlie (2nd)
This way David+ can play online on Cerebro and on Skynet, because his account has plus, and Charlie can only play online on skynet because the main account of the device has plus and enables all accounts of the device to enjoy the plus privilege of online play.
And yes: anyone of them can buy a game and download/play them on both devices.
You can't log on to the same PSN account on two PS3 machines at the same time.
You can have the account present on both PS3 machines, but as you've observed, once you (try to) log on the second PS3 you get the error message, and you'll have to log off the first PS3 before you can log on to the same (with the same account).
As such, you will not be able to be logged in on two different PS3 machines with the same account.
Best Answer
No, this isn't possible. The moment the second person logged into the same account, the first person would be forcibly logged out.
This has happened to me with my friends who have PS4s I've logged into in the past. It will kick your friend offline even if you're not playing online, too. (I was kicked out of a Dark Souls III boss when my friend was trying to do local multiplayer with a friend in Rocket League with my account)