Aromatic ring substitution: how are MNT and DNT further nitrated if nitro groups deactivate benzene rings?
On a industrial scale by using highly concentrated nitric acid known as fuming nitric acid (usually > 90%, but in the last step from DNT to TNT may also be anhydrous) along with oleum, which is a mixture of $\ce{SO_3}$ and sulfuric acid. Preparation in the lab may be achieved by more or less ordinary nitration at elevated temperatures. In a micro scale experiment [1] they used two different types of nitrating acid:


Nitrating acid I contains concentrated nitric acid 19% v/v, concentrated sulfuric acid 58% v/v and water 23% v/v.
Nitrating acid II is a mixture of concentrated nitric acid 25% v/v and oleum (30% $\ce{SO_3}$) 75% v/v.


Nitrating acid I was used for $\ce{Toluene -&gt; MNT}$ and $\ce{MNT -&gt; DNT}$ (65 °C). Nitrating acid II was used for $\ce{DNT -&gt; TNT}$ (110 °C).

1 The Stepwise Nitration of Toluene: A Multistep Microscale Synthesis Based on an Industrial Process
Richard A. Russell, Robert W. Swltzer, and Robert W. Langmwe
University College, University of N.S.W., Northcotl Drive, Campbell ACT. 2600, Australia