You have a couple of options, depending on your budget and how much of the Bose you want to keep. You can certainly get new components as suggested. It will require running some new wire alongside the OEM wiring and 99% some minor fab to make the tweeter fit the OEM pillar pod. I am doing something similar but I upgraded the woofers and installed them using rings I made from cutting board and foam baffles. Definitely more effortless bass and midbass sings, even with the front doors seeing less power - though I tweaked the balance for now to compensate. The Bose signal is clean, the tweeters sound good and don't need much power to do so, so they stay. They run off the same channel from the Bose amp and the crossover is like my CTS-V, just caps (bass blocker) inline after the woofer going into the tweeter. Next phase is installing a PPI 5 channel amp and console stealthbox with a CT sounds or Sundown 10. All signals will just be pulled from the Bose amp using an Audiocontrol LCQ-1 I had from my V. Not sure yet if I will put the front and rear both on the amp, bridge the front and rear channels to run only the fronts leaving rear on Bose amp, or split the front into active and upgrade tweets too leaving rear on the Bose. I prefer active setups normally but will determine that by listening. People in the know understand that the install (engineering) is more important than component selection. Bose is great at that, so that even with their low end component quality (especially drivers), you still get really nice sound at low/moderate listening. Here are the woofers I used:
https://www.parts-express.com/Dayton-Audio-GF180-4-6-1-2-Glass-Fiber-Cone-Woofer-4-Ohm-295-417
I have used pretty high end speakers, amps, HUs, etc. over the years - Alpine, a/d/s/, ED, ID, DLS, and done plenty of simple installs, midrange, and full 4 way active all out SQ builds. The technology has gotten so good and affordable that you can get amazing sound on a budget if you know what you are doing, plan carefully, and install properly. You just don't need to spend shit tons on the gear to have a wonderful listening experience.
For reference, I wanted a true factory looking install with no sub enclosure visible - that way I don't attract thieves' attention or lose luggage space. Granted, I already had the amp, LCQ1, and wiring already but I'll end up spending under $400 in equipment and end up with something that kicks ass with any kind of music anywhere except the SPL comp lanes. You could easily replicate this whole thing buying ALL new for under a grand. I know from experience this will still get loud enough to be uncomfortable in the vehicle and irritating to people around. GM could easily do this and make money on the option...I wish they would. Sound deadening would help but the OEM insulation is surprisingly quite good so I don't see the need right now, especially with the damping offered by the cutting board rings and foam baffles. If Bose didn't have that annoying bass modulation, I would just replace all the drivers including sub with proper impedance units...but it does and a decent substage makes a monster difference. Hope this helps. I have a Bose wiring diagram if you need it.