There is AT&Dx supported so it doesn't generate a ERROR response, but this does nothing. You would have to disable RTS/CTS in order to use DTS/DSR. They are mutually exclusive, but dropping DTR will not hang up the modem. I can look into supporting this, but no systems so far require this. What exact computer are you using?
I am using the TI-99/4A and its 'big brother' the Geneve. Both systems utilize the same RS232 hardware/cards.
There are a number of TI cable variants, some more compatible than others depending on the needed signals. Here are the pinouts for my BBS software and terminal emulation software. Both use RTS/CTS and DTR functionality.
RS232 -- Modem Name
1 -- 1 Protective Ground [required]
2 <-- 3 Receive Data [required]
3 --> 2 Transmit Data [required]
5 --> 4 Request to Send [emulator only; hardware handshaking,optional]
6 - No connection
7 -- 7 Logical Ground [required]
8 --> 20 Data Terminal Ready [emulator only. &D2 required for this functionality,optional]
5 --> 20 Data Terminal Ready [BBS only]
19 <-- 8 carrier detect [BBS only]
20 <-- 5 Clear to Send [hardware handshaking,optional]
TI labeled the connector as if it was a DCE (modem), which often makes for a lot of confusion. There are simpler cables that may be wired for modem connectivity when handshaking and DTR functionality are not desired.
Both programs drop DTR low for a short period of time, which (with option &D2) causes the modem to disconnect and return to the command interface. DSR does not come into play for in this configuration. Hopefully this makes sense, and with luck I made no mistakes.