Yea, no problem at all. Reinfections with the new variants (including the British, South African, and Brazilian) are possible, although they are rare. This is also why vaccination is encouraged, if I'm not wrong, to provide more robust immunity than natural infections.
Even the variants are gaining a bit of vaccine resistance, so I wouldn't be surprise if previously infected persons get infected again with the new variant.
At the same time, however, I think immunity is more like a continuum. There may still be some level of immunity against the emerging variants, but perhaps not as robust as it would be against the old variants.
https://www.advisory.com/daily-briefing/2021/02/11/reinfection