Most accounting has gone to the cloud. But some of it can be your cloud (eg on a server on premises or on your own VPS server out on the WWW). Odoo ERP is really hard to beat. It has two flavours Open source (free) or Enterprise (paid with more features and support) The Enterprise version can be on premise (self hosted) or Cloud hosted by Odoo.
I run Odoo Enterprise on premise (on our own web server) and have extensive customisations in place. It is by far and away the best manufacturing system I've used. We have it fully integrated with our web site and shipping systems and I have a direct printing module of my own design. From a manufacturing order page, I can say print product barcodes and the Odoo server sends a print job direct to my Zebra barcode printer. If there are 200 widgets being made, it will print 200 labels in one mouse click. You tell it to check availability and it will show what parts are missing. Getting Odoo to order all of our fasteners based on reorder rules has been a godsend. It also allows definition of workstations and routing of manufacturing through them with time tracking (eg. plasma cutting, press brake, welding etc) It also supports make to order so a sale will create the manufacturing order.
For another alternative, you could look at Front Accounting (its free open source). I have used it and liked it but I did not use it for manufacturing at that time.