See Sefer Ben Ish Chai ??? ? ???? ????? ???? ?
He says according to the gemara should shouldn’t daven one after the other however now that the minhag has developed to do so those who do have what to be somech on. He clarifies you can only do it in a tzibur but not k’yachid.
There are a fair amount of sefardi shuls in Israel that do this (apparently based on this Ben Ish Chai) and it’s incredibly convenient. As Mik5 mentioned though you have to be extremely careful not to forget shema b’zmana