You can only increase your bandwidth by do linking/bonding with two phone lines, two modems, and a special ISP account if not using two accounts with something like DiamonMM Shotgun modems. (This is all done from one [1] PC with two internal modems or one Shotgun modem, not two PC's).
ICS (Internet Connection Sharing) is a different sofware solution allowing one PC to establish a connection to the internet (the connection could be multilinking two modems or a single dial-up modem, or instead it could use DSL/cable modems, or ISDN/IDSL, or T1/FrameRelay, fiber to the home . . . or any method of establishing communications to the internet from your PC that will use ICS). This one PC can then share this one internet connection with all other network clients needing internet access. This means more than one PC shares the one connection, dividing the internet access speed that any PC achieves when on the internet.
A single phone line (POTS - plain old telephone system) can support a single modem, but voltage signaling usually limits POTS modems to communicate at 53.333Kb/s or about 6.66KB/s maximum (It's extremely rare to get this speed on a dial-up).
If your ISP and CO (your phone company) could change signaling levels and compression standard equipment, they you could get a newer modem to match their capabilities to achieve greater speeds than 56K. Since the voltage levels are determined by regulatory agencies, the only other cabilities are to change compression standards, which is exactly what the v.44 standard does (found on some newer modems) usually also having the newer v.92 standard (compared to v.90). If your ISP doesn't have v.92/v.44 capability on their RAS servers, your newer modem will not be able to use the better compression techniques to achieve faster downloads.