I'm not totally convinced of the philosophy of not changing the off-peak 'Takt' in the peak. For instance, imagine there's demand for 2 trains an hour off peak but 3 in the peak. Say the off-peak departures are at xx43 and xx13. In the peak, do you keep the xx43/xx13 and have an additional xx28 or xx58 (creating an irregular frequency, and also, if several lines do it, perhaps creating a pathing nightmare) or do you switch to a different, peak 'Takt' and run the services at xx43, xx03 and xx23 between say 1643 and 1843?
A textbook Taktfahrplan is about more than just a clockface timetable, though a clockface timetable is a good thing on its own and is a major part of a Takt. The other part of it is connectivity - and for that you need compatible service intervals. So, if you want things to connect, you can EITHER choose a pattern of 5-10-20-60-120 minutes between trains on particular lines (the principle being that the 120s will connect with something on every line, while the 5s will connect with the other 5s etc) OR you can choose 5-10-30-60-120, OR you can choose 5-15-30-60-120. Basically, each interval has to be divisible by the previous one for it to work properly. (If you can't justify a 2 hourly interval in a Takt you have to start questioning if you need the service at all, though if you're going to do a semi-irregular service on something like the Far North or Conwy Valley it does at least help connecting with other things if the "minutes past the hour" in the hours served are the same).
The trouble with saying you're going to have Euston-Manchester at 00 and 30 off peak and at 00, 20 and 40 between 1600 and 1900, say, is that those trains don't reach Manchester until much later, so your 1840 from Euston is going to reach Manchester at about 2040, well into the time when Manchester has gone back down to half-hourly on its key lines - so it misconnects.
Therefore, no, you can't do that, or at least not if you're going to do it properly. Peak extras in a Takt have to be overlaid on the base frequency without change to it.
The best thing to do to provided added capacity in a Takt is to extend train lengths - but if you can't, just put an extra on, perhaps even give it a train category that signifies that it is that and is basically a point to point service - DB, for instance, often used to put extras on as "D" rather than "IC"/"ICE", and SBB tend to put them on as REs on lines where everything else is S/IR/IC(N).