When I was starting out as an independent consultant, I'd manually increase invoice numbers by a semi-random number (instead of +1), so it looks like I had many invoices/clients. Later I switched to a less predictable invoice format like "20220111-01".

I don't know if fudging invoices numbers was helpful, but I'm pretty sure that sending "invoice+1" to the same client several times in a row is never positive signaling for independents (at best, it's neutral if no one looks, but it could be negative).