The answer depends on whether you have the M1 MacBook Pro or the Intel version.
M1 Macs
M1 Macs officially only support 2 monitors, for the Laptops this means one external and the internal screen. This is the same for all M1 macs, i.e. the 13" MBA, 13" MBP (M1 version), MacMini and iMac 24".
However, there is a workaround called DisplayLink. It does work, however, it needs special software and hardware, which means it may break at some point due to lack of support (this is very unlikely in the near future though, it seems like it gains more and more features right now, since there are still some limitations like rotating a screen).
Intel Macs
Depending on what exact model (13", 15", 16") you can usually connect at least two external monitors, the more powerful 16" version can even handle 4 monitors. You mention you have a 13" MBP, which means you can only connect up to 2 external monitors.
Connecting more thant the officially supported amount of monitors is again possible with DisplayLink or with an eGPU.
Remember, every pixel your MBP has to render puts more strain to it and will lead to higher CPU/GPU usage. Of course, maybe you need 4 monitors, but it seems like the "small" 13" MBP can't handle that. I have a 2017 15" MBP with a dedicated GPU and if I charge it and connect a 4K monitor it quickly starts ramping up the fans (depending on the workload), which might not be ideal, too.