Occasionally when cross-referencing stuff I will go up to perhaps 5 or even 10 in extreme circumstances, but then - as before - I close the tab when I am done.
For stuff I want to come back to "later" I just use a bookmark instead of just leaving it open.
At work I tend to leave email chat and calendar open all day, but that is only an extra 3 tabs.
In my experience - both at work and at home - it is better to concentrate on only a small number of things at once and try to work them through to completion (or as far as you can get) so you can just drop it from your head when you are done and not need to dedicate and brain energy on juggling all these differen "in-flight" tasks. I find it easier to concentrate and way more productive to finish a task and then move on, rather than context-switching every 2 minutes and wasting endless time hunting for "that tab with that thing I need" on it.