Idk why i write this nonsense, don't even bother to read as it's just my personal satisfaction. Factorio really mess me up.
It's possible to scaling either vertically or horizontally. But, for horizontally i think it should be like a flip-flop method (if that's what's it called), if the first lab direction of conveyor is from Bottom to Top, then the second layer of lab (right or left, didn't matter) should direct from Top to Bottom, then third layer should be like the first, vice versa.
To scaling you didn't need a second or third gate, so get rid of that if you doesn't need another SP input gate. Another intended design by me is to crossing the Left-side SP Lane (first layer) to the right of RIGHT second layer, this mean that the RIGHT second layer will use the Right-side SP Lane (first layer) as shared. The same for LEFT second layer, crossing the Right-side SP Lane (first layer) to the left of LEFT second layer, shared with first layer on Left-Side SP Lane.
Still on horizontally, for the Middle SP Lane (first layer) you will need three splitter, make a triangle, then it should be distribute equally for each direction, figure it out.
Keep in mind, that i find it only realistic to scaling horizontally into two layers, above that will need to split each of SP Lane on two direction horizontally, by itself is not a problem but the design will not compact and against philosophy of this blueprint in the first place.
Suggestion is to combine the scaling direction, you can scale vertically as many as it is possible for you, but limit scale horizontally only to two layers, as it is enough to triple the amount of lab. Or is it? As I'm writing this maybe there is another better option, i will update after next session.
(+) You can change the conveyor, splitter, etc. to their better version, of course.
(+) I see no point to use higher capability inserter, as it is fast enought to fill 12 SP before the research completed. But, why not?
(+) Also, you can remove fast inserter in conveyor gate, as i design it initially to be used with Locomotive/Train, but it is flexible.
I acknowledge that it's possible to even get more SP Lane with little improvement, at the least is 2 more SP Lane which is 16 SP. But with the same trick that been used in Middle SP Lane, we can adding 2 extra lane, and now it will be 20 SP. This trick theoretically will improve capability from each side of 3x3 lab to get input from 4 lane, not only 3. So the maximum is 32 SP for 16 lane. Will it compact? Surely a hard task to do.
It is my preference to use conveyor, and yes i see other approach that only use inserter, and thats much more compact than this. But, i like the feel of industrial, not molesting with inserter.
Note: I haven't test any of the information or suggestion i provide, but i'm pretty sure in my experience that's how it will work, i hope. I'm not even get out from Nauvis yet.