We first look at this chart of leading century-makers in Tests:
Most of the leading century makers such as Tendulkar, Kallis and Ponting have scored centuries in all 4 innings, though Steve Waugh made 32 centuries without any in the 4th innings. You can see that most of those in the above table did not do too well in the 3rd and 4th innings, though there are exceptions such as Sangakkara. Let us see if there are any who did equally well in all 4 innings. One has to go quite low down the table to find someone who scored one century in each innings (1111). The only such player was the South African Alan Melville. What is more odd is that these 4 centuries were in successive innings (though World War 2 intervened between the first and the second centuries)
You can see the full details here: http://stats.espncricinfo.com/ci/content/records/282968.html
When he returned to Test cricket in 1947 he scored centuries in both innings, then one more and no other century in his career. He thus equaled the record of 4 centuries in successive innings set by JH Fingleton. Soon afterwards, Weekes surpassed this with 5 and many years later Dravid also made 4 in successive innings.
If we go to those who scored 8 centuries, there is no one with an equitable 2222. The nearest approach would be by B Mitchell (SA) with 2321, CC Hunte 2312 and at a stretch DM Bravo (1331).
For those with 12 centuries, the closest are: AI Kallicharan (3531), AR Morris (5322), Ijaz Ahmed (3522) and JG Wright (4431). Also note Hanif Mohammad and JH Edrich with 4440.
16 centuries: H Sutcliffe (6433)
20 centuries: GA Gooch (7373), ME Waugh (7922), PA de Silva (5771)
24 centuries: GS Chappell (7-11-5-1), IVA Richards (8-10-4-2)
28 centuries: HM Amla (12-6-9-1)
32 centuries: AN Cook (8-10-12-2)
36 centuries: R Dravid is the only one, with a rather asymmetric 15-15-5-1.