Since OP has not mentioned the PHY being used, taking Micrel KSZ8021RNL/8031RNL as an example.Please look at the electrical specifications of the PHY
. You can see the differential output measured after 1:1 transfer lies between min. 0.95V to max. 1.05V, which is not the -ive voltage. For more details of the PHY electrical specification you can look page #33 onwards of KSZ821RNL datasheet.
With this I just wanted to highlight that differential signal need not always swing between positive to negative voltage. It can swing between more positive(say 3.0V) to less positive( say 1.0V), this will also be considered as differential signal.
For the basics of differential signalling you can look into app note from Lattice semiconductor, which also talks about advantages of differential signalling.
There can be many more levels for LVDS as shown below:. The image source is Analog Devices application note AN-1177. And this also talks about multipoint LVDS.
Now coming to MAXIM MAX4890/MAX4891/MAX4892 LAN switch, you can easily use this switching between two ethernet RJ45 to a single PHY, as it shown as an example circuit page #39 of the switch datasheet, image for reference below:
As a suggestion just make sure both your PHY and this LAN switch operate on the same voltage. And make sure to have a closer look at their logic levels as well.