.... and the huge label slapped in the middle of the back of the machine.

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If it's a 128 or 512 upgraded to a Plus, they have to install a new back in order to accommodate the SCSI part. So it will probably say Macintosh Plus on the back, and not what it used to be. The front will say nothing. The only way to tell is to enter the serial number into this page: http://macfaq.org/serial.html

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Yeah, If I remember correctly, the 'PLUS' upgrade included a rear case..that accpted scsi etc..and read Mac Plus (etc) I don't remember

if apple also replaced the front case..where the original 128/512

simply had the apple and the plus had the little apple (that pops out with a paper clip ) and the front reads Macintosh PLUS

A few of the early macs did get upgraded...with this costly (at the time ) apple upgrade..