Ok did some digging around the FAQ section and it says this about layaway.
"90 day layaway orders will be capped at $1600.
Our 180 layaway option has been temporarily removed."
So they have a dollar amount cap rather then an item limit cap, so as long as your total cost of the items stayed under $1600 you could have as many items as you want on layaway. The layaway option is still limited to only selected items though, and most are team buds only.

Patrick, yes to both questions. Buds Team Members can have up to 2 open no-fee layaway orders at a time. For regular Members Buds will charge $10 fee after 30 Days and another $15 after 60 Days for a total $25 layaway fee for a 90 day layaway.

Patrick, the simple answer is 'yes', you can have more than one gun on layaway at a time.

Right now buds has suspended most layaway, except for teambuds members, and even with team buds layaway is limited to eligible items (it will say layaway team buds only above the "Add to wish list" button). Its due to very high demand and low supply More info on teambuds here budsgunshop.com/teambuds.php  />And while buds may bring back regular layaway eventually there is currently no eta on when that might happen.
As far as multiple layaway items I don't believe so but I've never tried.
You might also consider financing the rifle through buds financing partner Credova budsgunshop.com/credova_financing.php />If you find a layaway eligible item add it to your cart proceed to check out and layaway will be a payment option, sleet this and follow the prints, your item ships after the last payment is made.