Anyone know the weight limit for a 4x4 Kallax with undeframe?

Right @tonyptony, but you’re looking at the single-cubicle model; the 4-cubicle model diagram shows an internal height and width of 12-5/8" (1/8" shy of 12-3/4"), but mine are just shy of 12-3/4" (like 12-11/16"). The 2-cubicle EKET has the same internal height as the 4-cubicle IF (and only if) positioned vertically; positioned horizontally each cubicle has an internal height of 12-1/4" (which is the width of each cubicle when positioned vertically). Confused? ;-) At any rate, the best value EKET model is the 4-cubicle version ($50 when I bought mine, now $60), and they have sufficient height for LP’s, even boxsets (though just barely. The Kallax has a little more).

With a back panel added (or even just a left-to-right brace or two), the Kallax will be great. And the underframe is made of solid wood, so should have no problem supporting a fully-loaded 4 x 4. For piece of mind you could consider adding a middle leg front and rear. A simple block of pine cut to length would do the job, or go nuts and use oak. ;-)

Actually, the EKET's internal height is 12-3/4", as is the width of each cubicle. The depth is 13". I have a fair number of boxsets, which fit in the EKET just fine. The only ones too tall for it are the MoFi 1-Steps and Analogue Productions UHQR's, but those have the LP's themselves in normal-sized cardboard jackets. I store the over-sized boxes in a bookcase; even if those boxes fit, I wouldn't store the LP's in them anyway: too much work to get the LP out every time. ;-)

One thing you absolutely want to do with the Kallax is to set it up with the full-width panels horizontal; the 4 x 4 version can also be positioned such that those panels run vertically. Some Kallax owners have not noticed that structural design element, which has led to some catastrophic LP-loaded collapses! Some owners have added a back panel, which not only keeps dust out of each cubicle, but also provides some additional structural integrity.

I don’t know about the Kallax, but I have my Ikea EKET cubes sitting on the underframe Ikea made (now discontinued, replaced by individual feet) for it. The 4-cube EKET is 27.5" wide, and I have three EKET’s on each underframe, so 12 cubicles total on each frame

The EKET has holes drilled into the back ends of each (top, bottom, and both sides), made for installing brackets (sold as an accessory option) that secure one cube to another. My stacks of EKET’s are so secured, as well as to EKET’s on either side---three 4-cube EKET’s tall, five wide. The EKET also comes with adjustable spacers that are attached to their backside, for stabilizing each to the wall behind them. Each underframe foot (and the individual feet) is also adjustable, so I have the stack of EKET’s leaning just slightly towards the wall, the adjustable back spacers making contact with that wall. My assembly of fifteen 4-cube EKET’s feels like it’s part of the room’s structure; absolutely immovable!

What you might consider is adding another leg in the middle of the Kallax underframe, front and rear. That will of course provide support in the middle of each underframe, the weak point in the frame. If you have yet to assemble the Kallax’s, take a look at the EKET. I compared the two on the sales floor, and found the EKET to be more structurally stiff than the Kallax, with the bonus of each cubicle being an enclosed space. The EKET has a back panel, the Kallax does not. With an open back side, dust can get to the open side of your LP’s. If you have your LP’s in plastic outer sleeves, perhaps that’s not a problem. Another EKET advantage is the shallower depth; the EKET is only 13.75" deep, so doesn’t have the excessive space behind the LP’s that the Kallax does. In the EKET, the LP’s come right to the front edge of the cube.