Status of the next four:
“Ununennium, also known as eka-francium or element 119, is the hypothetical chemical element with symbol Uue Experiments aimed at the synthesis of ununennium began in June 2018 at RIKEN in Japan; another attempt by the team at the Joint Institute for Nuclear Research at Dubna, Russia is planned to begin in late 2020.”
“Unbinilium, also known as eka-radium or simply element 120. One 2011 attempt from the German team at the GSI Helmholtz Centre for Heavy Ion Research had a suggestive but not conclusive result suggesting the possible production of 299Ubn, but the data were incomplete and did not match theoretical expectations. Planned attempts from Russian, Japanese, and French teams are scheduled for 2017–2020. Experimental evidence from these attempts shows that the period 8 elements would likely be far more difficult to synthesise than the previous known elements
“The team at RIKEN in Japan has plans to attempt the synthesis of element 121 in the future after it attempts elements 119 and 120.”
And more and in more detail at https://en.wikipedia.org/wiki/Extended_periodic_table#Synthesis_attempts
There have already been synthesis attempts up to element 127.