This is what I did to my new UT61E. I think it is a simple and good DIY to share. What it does, in addition to the usual APO DIY, is to provide manual power on/off controls at any ON positions of the rotary switch without turning the switch (as other had already asked).
----The operations:
1). When the meter is on, pressing "hold" for 3 seconds to turn the meter off.
2). When the meter is off, pressing "range" to turn it on.
3). The normal "hold" and "range" functions are retained.
4). The APO DIY worked better (smaller off current).
5). Switching the rotary from "OFF" to "V" no longer turn on the meter. I do not feel the need to to retain this function, but if desired probably adding a cap somewhere should have it work again.
----The performance:
1). The off current is about 0.01uA.
In fact, the usual APO DIY by itself has severe problems in that the power off current is about 170uA (my test). For a 200mAh battery, this translates to about 1.5 month power retaining time without using the meter. To give an idea about how small 0.01uA is, it could be mentioned that the leak current of a Li battery with 10 years of shelf life is around 1uA.
2). The burden voltage is about 0.2mV.
3). This power on/off ctrl worked properly even when the battery is < 3V (did not test the meter accuracy at this voltage).
----The making:
Except for the Si4562, all other parts are taken from junk PCBs I had (a few). That is why you see SMDs of different sizes. I bought Si4562 on ebay for about $0.35 each, but I had to buy 10 for this price. I also made a few goofs: cut a wrong trace on the meter PCB; broke a leg of the IC; a few wiring changes after soldered it to the meter and along the way burnt a corner of the res array.
Altogether, 2 traces on the meter PCB needs to be cut: the VB+ trace and the "range" button trace. The board needs only to be about 4x5 pads in size.
If you want to try this, make sure D1 has enough forward voltage drop or simply place 2 diodes or a zenor instead.
On a related note, for the APO-data link part of the DIY, the pull up resistor is not really needed. According to the datasheet, the RS232 pin was internally pulled up with a short current about 10uA. One can regard this as a resistor of a few hundred k connected to the positive voltage (~3V) rail. I used the photoresistor+red LED approach without the extra resistor.