Most definitely. I, however, don't have that choice, apparently we need the router from the ISP for it to even work.
I hope to one day build a pfsense router though, and just use the current one as a bridge (hoping that's possible)
Modem or router?
Routers tend to be universal, modems are actually far more universal than people think, and a combo unit is no different. Modems rarely have upgradable firmware.
Not sure about where you live, but in the US we forced standards on the bastards so you don't have to use your providers modem, they will sometimes tell you that and the installer may even believe it, but you should be able to use any standard off the shelf model that is compatible. Mostly likely all you need to do is register the modem (mac address I think) with them so their system will allow it access. Even if your country didn't enforce a standard, odds of your carrier getting something custom for them is slim. From there you should be able to use any router. You can call and ask then what modems are compatible or what standard they use (docsis 3.0 is most common) then just buy what you want and then use your own router (can also just look up what you currently have and see if it uses a common standard then find compatible ones). I got a list from my provider, figured out the standard and bought what I wanted, paid itself off in a little over a year.
They may be using a business class modem, which may need you to manually input the routing settings as well as register it with them, but it's not difficult to do (load up the config web page and plug them in, then a reset).
If you have your phone landline, tv and internet from one provider, you will have another box as well for the phones. That one you probably will not be able to get rid of.
My home system is their tv/cable breakout --> my modem --> my router --> switch (for more ports)
I won't use the provided modem or modem/router because 90$% of the time, they are garbage, or outdated. For example, wireless N had been out for 2 years, they were still shipping modem/routers with wireless G and often 10/100 ports. And of course the lack of ability to tweak settings like ports and things is a hassle.