While we're waiting for the experts, here's a word from a user.
I hope I understand your question.
(Note firstly that some of the 3000 series scopes use 12-bit quantisation, so depending on your needs, they might be suitable already.)
The issue is that you don't want to "waste" headroom on the chosen input range?
If your signal is from zero to +3 volts, and you selected a range -5 volts to +5 volts, you would be "wasting" 70% of the range.
There might be two simple things that you could try. The first would improve to a wastage of 50%. The second (less likely to succeed) might reduce wastage to zero.
You might be able to regain part of the range by attenuating your signal so it just fits into a lower range, namely -2 volts to +2 volts.
Effectively you would be making a special probe.
Depending on your signal you might be able to simply include a half megohm low noise resistor. This would be in series with the specified one megohm input impedance of the scope, attenuating by one third your signal voltage, and reducing your maximum excursion to +2 volts.
You could then use the Pico feature of "custom ranges" so that the software displays correctly your signal voltage.
You could try to regain all the remaining wastage, if you could float the ground voltage of the scope together with its attached PC. You should only do this if you understand its implications. Also you would be able to use more than one channel only if all channels shared a common zero volts from your signals.
Still using the half megohm resistance probe, you could change the range on the scope: select -1 volt to +1 volt.
Your signal from zero to +3 volts would then be seen by the scope as -1 volt to +1 volt.
Once again the marvellous "custom ranges" could be used to clarify the display.
No wastage at all. But something might get seriously damaged unless the scope/PC were battery operated and isolated from any "ground" in common with your source.
This is only my opinion and I welcome any weakness in the analysis.
EDIT: I had another think about this and I don't think the second part would work. You would have to ensure that the "ground" of the scope/PC was exactly 1.5 volts above your 0 volt level. It would be subject to a lot of electrical noise. You might make it work by AC coupling your signal (not internally in the scope but with a suitable capacitor on the probe).
I don't think you would ever be successful with other than a single channel.
Unless you go for a complicated "active" probe, I think you have to live with 50% waste (1 bit) due to the disused negative-going part of the input that the scope sees.
Regards to all,