Can I hook a dishwasher into my washing machine plumbing?

I just bought my first house. I have a small kitchen. I want to put in a dishwasher, but there's no room for a built-in. Since I have a stacked washer-dryer combo in there, I have an open space for a portable type dishwasher next to them. There's hot and cold water, and a standpipe for drainage.

Can I hook a dishwasher into this?

What can I do to place the drain hoses from both appliances into the standpipe at the same time?

The washing machine generally cannot share a standpipe...for the very good reason that it would overflow if both ran at the same time.