Many 486 PCs (old) and all Pentiums (or the like) should have modern 16550As (usually called just 16550's) with FIFOs. If you have something really old (pre 1990), the chip may unplug so that you may be able to upgrade by finding a plug-in 16550A chip and replacing your existing 16450 UART. If the functionality has been built into another type of chip, you are out of luck. If the UART is socketed, then upgrading would be easy if you could find a replacement. The new and old are pin-to-pin compatible. It may be more feasible to just buy a new serial card on the Internet (few retail stores stock them today) or find a used one.
Modern kernels should not allow the opening of ports with the same IO address. But one may probe for ports even though they are not open. If two ports have the same IO address then old fashioned probing by sending commands to the address will erroneously indicate only one port. But modem device detection at boot-time should discover both ports and report the conflict. In olden days, all sorts of errors were reported/observed for devices illegally attempting to use the same IO address. See Probing.
In the past, to get a certain serial port supported, one might need to modify the C source code, perhaps by adding a #define to it. Today, the use modules for multiport cards, use of parameters for modules or the kernel, or the use of configuration options should handle all cases.
For a modem to transmit at nearly 56k requires that it be a special digital modem and have a digital connection to a digital phone line (such as a T1 line). Modems used with serial cards (the modems may either be on the serial card or on another card) normally have no such digital connection so they can't be used at the 56k speed, and thus are obsolete unless one doesn't need to send at 56k. In other words they are obsolete for ISP servers but might be OK for small business or home use.
An partial exception to the above are modem banks that connect to multiport serial cards where the modem bank can access multiplexed digital phone lines. Thus one could use a multiport serial card with a few 56k digital modems for sending at 56k. For both analog and digital modems there is one modem on each serial port so there needs to be an external cable (modem bank to multiport) for each modem. This can lead to a large number of cables. So it's less clutter (and cheaper) to use internal modems without a multiport card. This makes even this "exception" obsolete for high volume work. It's somewhat analogous to the lower cost of an internal modem for a desktop PC as compared to the higher cost (and more cabling) for an external modem. See Modem-HOWTO: Modem Pools, Digital Modems.
END OF Serial-HOWTO