Can I put 700x32 tyres on my Avanti Blade?
If you've got 28 mm tyres on there already, you should be better placed to tell than anyone who hasn't already fitted 32s.  Just check that there's a few mm clearance at the sides and top/front (in theory you only need 2mm extra either side but you need a little spare room for flexing, different tyres coming up a diffewrent size etc.).  From Sheldon Brown's width table you can see it would be a rare rim that couldn't fit 32s if it could fit 28s, and he admits the table is rahter cautious anyway.