The consensus in this thread is the part I would follow most closely: tier building still has a place, but only when Tier 1 is genuinely strong. SadiqArshad put it well, and Garlick's first check is the right starting point, because there is little point adding layers to a Tier 1 page that is not indexed or getting traffic on its own.
For the question about how many tiers to use, I would stay at two, as blackfighter01 and Muhammad Shakeel suggested. I would use Tier 2 mainly to help Tier 1 get indexed and to support a page that already makes sense, not to chase a ranking jump from the whole structure at once. That also means keeping anchors varied and the Tier 2 pages relevant, rather than blasting a large automated set, which several replies here, including Renata Solis and Lucas786, warned against with tools like GSA and RankerX.
A practical check I use is to separate the two measurements: first, is the Tier 1 page indexed and does it get impressions, and second, is the target page itself actually moving for its intended keywords. If Tier 1 is weak, fix that first. If Tier 1 is solid but the target page is not moving, the problem is more likely the target page, its content, or its keyword choice than a missing third tier.