The break-up we are referring to occurs in the power section of the amplifier. As the amplitude into the power amp increases (ie getting louder), it reaches a certain point where the output signal starts to clip, in more common terms, distort. The lower the power rating of the power section, the earlier the clipping occurs. In a jamming environment, you may have to max out the volume of the power section in order to be heard over everything else. And of course, by then, your signal has already distorted to lovelovelovelove and back.
The power section of the amplifier is located in the entire signal chain after the effects loop, where is the last place that you can place your volume pedal, doing so only reduces the amplitude of the signal before that.
You have to understand what you want to get is able to achieve the outcome that you want. In this case, it isn't going to get you what you want. So, either you raise your budget, or you stick to what's available in your means.