Yes. The Tesla Mobile Connector can be fitted with a wide range of Level1 (120V) and Level 2 (240V) power plug adapters. The majority of the third-party equipment available from Amazon, eBay, etc. will have the option of supporting 120V charging using the NEMA 5-15 plug adapter and at least one 240V plug adapter (e.g., 6-20, 14-30, 14-50). Depending on where and how you plan to use the mobile equipment to charge (at home, when camping, traveling, etc.) the third-party solution may be adequate. (Every Tesla vehicle comes with a small accessory, the Tesla SAE J1772 adapter (or just called the J1772 adapter) that you would use to be able to charge using third-party (non-Tesla) Level 1 and Level 2 charging equipment. This includes using a public Level 2 charging station that are often found in public buildings, garages.
If your home was built recently you may already have a NEMA 14-50 receptacle for 240V/50A charging. There is almost certainly a NEMA 5-15 or 5-20 receptacle already located in the garage that you could use to charge with the correct power plug adapter.
Until you sort out your home charging needs you can use the Tesla Supercharger network or a public Level 2 charging station (download the Plugshare app onto your phone to locate nearby public charging stations.) You can also use Google Maps to located Electric Vehicle Charging, Tesla Superchargers (Tesla's high power DC charging network) and Tesla Destination Chargers (Level 2 fitted with a Tesla charging connector.)