There is no problem when streaming from different services. Individual services may limit how many concurrent streams you can use from them at one time. My Acorn account, for instance, says I may only stream 1 at a time.
- Roku Streaming Stick +, 3810X, Ser YH0059427035, wifi - Samsung UN55ES6100
- Roku Streaming Stick, 3600X, Ser 5S56D8240827, wifi - JVC EM37T
- TCL Roku TV 43S425/C107X, Ser X000001R60KV, wifi