I wouldn't try an attach a bin cage to the cage. As the others say - one larger floor area is better. If you've only had him 3 weeks I would ask for a refund for the Rosewood cage. It can be difficult to find a bin big enough that doesn't cost too much.
There is a very good RUB bin - not too big not too small - but it costs about £40 something and you can buy an Alaska cage for £34 - which would be great for a Syrian! It looks a bit bare but has space for an 11" or 12" wheel and plenty of toys - shelves and hammocks etc to give added enrichment. It does need a house though - the little white one on the shelf is no good for Syrians - it could do with removing really as the holes are too small.
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The Barney cage is also great for a Syrian and is on offer at the moment. About £10 more than the Alaska and it comes with a good house, a shelf/level and a basic 8" wheel - so all you would need would be toys and water bottle/food bowl.
Barney Pet Cage | Great deals at zooplus!
The Barney cage has narrow 7mm bar spacing so is quite futureproof and could be used for dwarf hamsters at some point as well (if set up right).
Both are still a bit on the high side but as long as you have lots of substrate and he can't land on anything hard if he decided to monkey bar across the top, then they're both fine.
I have the Barney cage - our Syrian loved it. You can make a whole extra level with tubes and sputniks, which is safer than climbing to a height and falling
I added an extra shelf along the back and tied a rat sized tube across the top between the shelf and a rat sized sputnik which was over the main shelf - so he could run around at a higher level as well as ground level.
