Own more then one freighter

There are three paths available to you: Explore Freely, Journey to the Center, or the Atlas Path. This is made clear when encountering a Space Anomaly, where you will be given the choice to be given a technology (helping you to Explore Freely), have a black hole marked on your map (aiding you in Journeying to the Center), or be directed to the nearest Atlas Station (pointing you down the Atlas Path).

To "follow" the other two paths, either explore whatever stars you like, or head directly for the center, making use of black hole jumps where you can.

From the No Man's Sky Wiki:

Freighters have a maximum storage capacity of 48 slots and the first freighters encountered have 13 slots. Once a freighter is purchased, the freighters the player encounters from then on will have 2 additional storage slots and cost about 2.5 million credits more than the last until the cap is reached.

Another Wiki states similar information:

Freighters can be upgraded in the same general manner as individual ships, with each upgrade adding a slot or two to what your current freighter contains (cost per upgrade will be roughly 2.5 million units).

The first one will always have 13 slots and there isn't a free one to begin with. The next one you buy will have 1 to 2 more slots and this continues until the max is reached. The price goes up by about 2.5 million credits each time you buy a new freighter.