Multiple JR Train Pass Purchase

Is there any restriction to purchase JR Tokyo Wide Pass and JR East Tohoku Area Pass at the same time but use at different intervals?

No.

The only restriction I know of is that you can not have two of the same pass for the same person for the same start day - and why someone would do that is a mystery anyway.

I don't see how this would make sense, however, seeing as for both passes the validity period starts on the day of purchase and cannot be changed.

I can see it could be quite a good combination - 8-days travel for 30,000 yen. JR East passes give any five days within 14 days and the three day Tokyo Wide pass could be used within that period. You could do Tokyo-Aomori-Tokyo then time in Tokyo on the 3-day pass, before another trip like Tokyo-Gala Yuzawa-Tokyo. However, doing back-tracking or longer distances jut to make the passes pay off isn't a saving. Depends on the actual schedule being considered.

both passes the validity period starts on the day of purchase and cannot be changed.

It is correct for the JR East Tohoku Area Pass. However, correct me if I am wrong, I vaguely recall that I could nominate the starting date of the JR Tokyo Wide Pass.