While the rule books might vary a little in the specific detail, for heavies, one needs to ensure a number of requirements are met - runway, climb, obstacle, etc., etc.
Several ways to approach this, given that the work, itself, is pretty straightforward, albeit that the detail can provide for head scratching at times -
(a) the operator provides individual runway charts addressing all requirements and providing a limiting RTOW
(b) the operator provides general takeoff charts which the pilot can use to generate an RTOW using the input data prescribed by the operator. Generally, this will produce a weight somewhat less than (a), which is why commercial operators use (a) with (b) as the get out of jail backup.
(c) the pilot pulls out the AFM, gets all the necessary input data - that's the hard bit, usually, and does the sums. Time taken could vary from 10-15 minutes to a day or so. Generally, not a practical option, especially for commercial operations
(d) any variety of not so sensible ways to do it ...
Whether the aim is to use full thrust or a reduced thrust just adds another iteration to the process to end up with the limiting RTOW case.
Main thing is .. winging it on the day (ie "she'll be all right") is not a good idea and, sooner or later, is going to end in tears.