It depends. Presets are simply a "save" of the state of certain sliders (or all of them - it is entirely up to the preset). You could make an adjustment to adjust the temperature slider and "save" that setting as a preset. Any time you apply that preset, the temperature slider would just go to that position no matter what it was to begin with. In other words, it's not a relative adjustment. If the preset calls for 1500 degrees on the temperature slider, that's where it will go when you apply this preset regardless of whether the slider was at 1000 or 2000 before you applied it. Obviously, most presets are more involved than this. So, there is a good chance that applying a preset will override a previous preset's settings if the new preset involves the same adjustment as an old preset. In this case, the newer preset wins. For example, if you have a preset applied that affects temperature, contrast, clarity, and saturation - and you apply another preset that affects vibrance, shadows, highlights and clarity - then the new preset will override the old preset's clarity adjustment.
Also, it is important to understand that you are not really processing anything in Lightroom. All you are doing is giving the software a set of instructions - adjustments to make, and you are seeing these adjustments in real time. They haven't actually been applied yet. This is one big reason that programs like Lightroom are taxing on your processors. Every time you make an adjustment, you are changing the instructions, and the program runs out and looks at the original photograph, applies those instructions - and then displays what the result would look like IF you applied them. "Applying" them would be something like exporting to jpeg or tiff - as you say. And yes, if you did this, and brought it back into Lightroom, you could layer preset on top of preset regardless of whether those presets involve common adjustments, but you are losing boat-loads of quality by doing this. I'm assuming you are editing RAW files in Lightroom. As soon as you export and bring them back in, that is no longer the case.
One last thing - and this is probably the most important point. There is absolutely NOTHING that a preset can do that you can't do on your own manually. There is nothing special about them. To answer your question directly - is there a way to apply a new preset based on an already 'processed' version? No. Because presets are not relative adjustments. They are not "based" on anything. They are just save states of the positions of sliders.
The simple answer, export to PS with lightroom adjustments, as Tiff. Close PS, The new Tiff is back in LR with the previous presets baked in, then I can try the new super duper presets.
Not sure if creating a DNG also bakes in the adjustments?
A DNG is just Adobe's RAW file format. It won't do what you are asking. As I said, you could do what you are saying - export as tiff to PS, then immediately bring it back in to Lightroom, and then add a preset, but why? Are they RAW files? If so, then you are losing an incredible amount of ability to make adjustments. If they are JPEGs to begin with, then you're not going to get much out of it anyway. If you have PS and you want to do what you are trying to do, I'd say editing the whole shebang in PS would be better. You can just layer adjustment layers on top of each other. As I said before, there is nothing really special about Lightroom presets. They are just save states of the positions of sliders, so there is nothing a preset gives you that you can't do yourself. What exactly are you going for? What kinds of presets are you wanting to layer?