So if that is what's installed I am guessing you have the left front and rear spliced in parallel into the left channel so no front to rear and likewise the right. This will load the amp as mentioned earlier and it will run hot as each channel is driving the pair of speakers and driving 2ohm load.
Perhaps one option is to replace it with a more complete unit.
1. Amp for four channel with front/rear and left/right individual outputs.
2. Bluetooth input to connect to smartthingy for all music and radio/waze etc.
3. Other inputs in case you do want to wire something in later.
4. Compact to fit into the same place and use the existing speaker cables (or replace them with heavier duty using the existing to pull them through)
5. What are you going to use to trigger it on and off, do you want a manual power or just Bluetooth listen-for-phone as trigger. You may want to inspect the power feed as a result. Ensure there is a good fuse in line even if there is one on the amp!
https://youtu.be/qj4BqMXHCtQ (warning - among the most annoying background music and presenter combo I have seen in ages....)
https://www.amazon.co.uk/Soundstream-ST4-1000DB-Stealth-Channel-Amplifier/dp/B01B9KH1S8Might be an example but not specifically a recommendation. Just to see if this is down the right track?