Thanks to commenters Cassander, Kirk, and Michael for the material below.
I'm including Texas in the total number of 18. Texas' complaint can be found here.
Missouri has filed an amicus curiae brief in support of Texas' complaint, and was joined by 16 other states: Alabama, Arkansas, Florida, Indiana, Kansas, Louisiana, Mississippi, Montana, Nebraska, North Dakota, Oklahoma, South Carolina, South Dakota, Tennessee, Utah, and West Virginia.
The conclusion of the Texas complaint states, in part:
Although this Court’s original jurisdiction precedents would justify the Court's hearing this matter under the Court’s discretion, ..., Plaintiff State respectfully submits that the Court’s review is not discretionary. To the contrary, the plain text of § 1251(a) provides exclusive jurisdiction, not discretionary jurisdiction.[(a)The Supreme Court shall have original and exclusive jurisdiction of all controversies between two or more States. 28 USC 1251(a)]
The issues presented here are neither fact-bound nor complex, and their vital importance urgently needs a resolution. Plaintiff State will move this Courtfor expedited consideration but also suggest that this case is a prime candidate for summary disposition because the material facts namely, that the COVID-19 pandemic prompted non-legislative actors to unlawfully modify Defendant States’ election laws,and carry out an election in violation of basic voter integrity statutes are not in serious dispute. ... This case presents a pure and straightforward question of law that requires neither finding additional facts nor briefing beyond the threshold issues presented here.
Leave to file the Bill of Complaint should be granted.
Here's the conclusion of the amicus brief:
The allegations in the Bill of Complaint raise important constitutional issues under the Electors Clause of Article II, § 1. They also raise serious concerns relating to election integrity and public confidence in elections. These are questions of great public importance that warrant this Court’s attention. The Court should grant the Plaintiff’s Motion for Leave to File Bill of Complaint.
I find these arguments compelling. I can't conceive of any reason for the SCOTUS to refuse to hear the case. Especially when the case is supported by 18 states, led by Texas.
UPDATE: I hear we're up to 22 states now.