Thomas is exactly right. Here's the principle: TXP compresses the shadows and expands the highlights. It continued the long line of Kodak's "Portrait" films. To make Tri X or TMY look like TXP, you need to depress the shadows and lift the highlights, just a little.
This isn't speculation or theorizing. It works. It's pretty old school photography, but it works.
The first thing is to get a copy of Minor White's "The New Zone System Manual". White, Zakia and Lorenz give you all the basic information you need to pretty much figure out out to make a film do what you want to.
Next, think this out. WHAT are the developers we all like for lots of shadow detail, great midtones, and gentle highlights ?
(What we used to call 'soft-working developers').
D-76, XTOL, D-23, Microdol X, Microphen, DDX, T-Max Developer, etc., etc., etc. Metol/HQ, Phenidone/HQ, Ascorbate developers.
You don't want these.
To pick up Thomas' post, Edwal 10 and Edwal 12 were made in the '30s to give normal negatives in Midwestern murk.
Edwal 10 is a variation of D-76, that uses Glycin in place of HQ. It reproduces the classic Kodak Portrait Pan curve on TMY2. Edwal 12 is a super fine grain version of Edwal 10. It isn't everybody's cup of tea, because it uses PPD, which activates the glycin at a very low pH to work as if it were in a Carbonate solution. Either E10 or E12 will give reliable and beautiful results. You have to mix it yourself, and it wants replenishment. If you are a one-shot photographer, look elsewhere. But if you want to use TMY 120, I'd recommend Edwal 10 and 12 without hesitation. Edwal 10 and TMY gives you TXP, but finer granularity and higher definition. Edwal 12 has been my own little way of shooting 35mm TXP for 25 years. Shhh. It's a secret because it will make your 120 prints look like they came from 4x5.
HC-110 and DK-50 are very similar,and will give a mild TXP experience, similar to souping TXP in Xtol. If you have been using HC-110 in TXP, you need something more aggressive.
Isn't this fun ?
If you need strong highlight lift, and DK-50 isn't quite what you want, use DK-60a. You won't find it on the shelves, but it is easy to make up.
Formulary offers MCM-100. Ought to do it, just fine. PYRO TRIETHANOLAMINE will do it.
Pyrocat with a little more B will do it.
Dilute Dektol (1+10 ) or LPD or Bromophen will do it. Don't panic about using a 'grainy' print developer. TMY2 is pretty grain resistant. Polymax liquid developer, Sprint paper developer... probably lots of choices out there.
ABC Pyro, but probably not PMK or Wimberleys ...
Classic developers like Glycin Carbonate or Metol Carbonate will do it.
Beutlers, yes.
And Harvey's 777 will do the trick, but it will take a long development time to build the highlight density.
There are probably lots of other answers. Since most developers we run across are so similar in composition and result,
most of the things you see at digital truth won't help.
Oh, almost forgot my old pal Rodinal.
Some of these developers will want EI 250-320.
Some will want EI 400-800.
It really is no more than Photo 101, but selecting a different developer than D-76.
Good luck.