Can a 400e pull...?

Easily.  

The newer MTH "Tinplate Traditions" and LCT traditional 400E's have traction tires, so they should pull three or more state cars with ease.

I have a 2-400E "Lionel Classics" WITHOUT traction tires, and it pulls my three state cars (California, Maryland, and New York) once it gets started! 

sunrise, I use to pull all 4 state cars with a traditional 400e no problem.

Okay, wait, maybe not so easily.  I got thinking about it, and went over to the layout this morning and put some equipment on the track:

Here's my crackle black MTH 400E #10-1262-0 traditional (Build-a-loco motor) with 3 state cars.  The loco is wearing traction tires.  I apologize for the film, it's handheld and raw footage...

Now before we jump to conclusions, the place where it stalls is on an uphill 2% grade, which is not a common thing on standard gauge layouts.  On the level it pulls them okay... but I'm not sure it qualifies as "easily".  

Also, this is my only Traditional 400E, it is new, and it sounds to me like it needs some run time to break in: I think it's pretty tight and working against itself to some extent, another 400E might have more power.

For contrast, here's my gloss black Proto 2 400E, 11-1001-1, also with traction tires, with five state cars on, and this I would characterize as pulling them "easily".  Those can motors are a different breed of beast.

Yes it will but will have the obvious slowing in turns and grades. My original does well with 4 state cars as a comparison.

My MTH Ps-1 and PS-2 400's without traction tires run fine with 6 BC cars and a 200/500-box car in tow on level track with 72 radii. I think I can squeeze one more BC car out of them without Traction tires. Last year my boys and I ran a MTH PS-2 #384 with traction tires on our Christmas layout with 6 BC cars and the 200/500 boxcar and it didn’t even strain, we then put on 4 more BC style cars and it ran with not even a slip or groan. We never did find out the limit of that little 384.   

Obviously, the can motors in the Proto 1.0 and 2.0 locos have more torque than the less efficient open frame "BAL" motors of the MTH traditional locos.

My Proto2.0 Brute has two LARGE can motors, and even WITHOUT the traction tires (I replaced them with REGULAR drive wheels), it will pull the FOUR "Showroom" cars (12 pounds each) with ease! 

Comparing the MTH Proto motors and the BAL motors is like the proverbial "apples versus oranges". 

Beautiful layout and collection!