Yes, as you observed with shooters, layering your hearing protection is a common (and effective) way to increase your level of hearing protection.
The American National Standards Institute (ANSI) requires that all safety devices used for noise reduction be labeled with a noise reduction rating (NRR) to quantify their effectiveness. Even though NRR is expressed in decibels (dB), it is important to understand that hearing protectors DO NOT reduce the surrounding levels by that amount. You can do the math (see below(1)), but for the sake of this post, know that the higher the NRR number, the greater the capacity for noise reduction.
Layering Noise Reduction
If you are layering you hearing protection, it's also important to note that layering noise protection is not additive (i.e. 33 dB + 29 dB ≠ 62 dB reduction), nor is the noise reduced by a fixed percentage. The exact math is outside the scope of this post, but with your average safety device (with an NRR of about 20-33db), the math will work out to about 5 dB reduction with a second layer.
(1) For anyone interested in the measurements:
OSHA defines what noise levels warrant hearing protection to assure safe working conditions. Excessive noise is generally defined as exposure to 85 or more decibels of sound over an 8 hour period. But if the ambient noise exceeds those levels, the amount of time until damage can occur will decrease.
To calculate the noise reduction, you can get a pretty good approximation by taking the NRR rating, subtract 7, and then divide by 2. For example, if you have a piece of machinery operating at 110 dB with hearing protection rated at 33 NRR, the reduction would look like this:
110 dB - (33 - 7) / 2
110 dB - 13
= 97 dB
You can then use the chart above to determine if addition noise protection is necessary.
There's obviously little downside to being overly conservative when it comes to protecting your hearing. I tend to use it even if I don't absolutely need it; it's just a good habit.
If you are occasionally working with something particularly loud, you can double up the methods of protection… but if you do this often, it is best to just buy one, convenient piece of protection that will handle those levels.
If you are concerned about blocking out the "normal" noises as a matter of safety (communicating with people, hearing alarms, etc), then you might want to consider investing in some good electronic ear protection (search). Devices like these will provide an effective reduction of loud noises while allowing (or even amplifying) the normal sounds you might want to hear. That's pretty cool.
I use electronic hearing protection almost exclusively. When I am working with loud equipment (or things that go <boom>), I want to be able to hear the things going on around me. When the equipment goes off, I don't have to remove my hearing protection or remember to put it back on again. When it starts to get noisy, it's just there. And I like to assure that I can continue to communicate normally with the people or things around me.